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O P T I M A

55

OCTOBER 1997

Mathematical Programming Society Newsletter

The opening session was held onMonday, August 25 in the MétropoleConcert Hall downtown Lausanne.Tom Liebling called the meeting to or-der. Welcome addresses were also givenby A. Bidaud, President of the CityCouncil of Lausanne, J.-C. Badoux,President of the EPFL, and Dominiquede Werra, Vice-President of the EPFLand International Advisory CommitteeChair. Plenary talks were given byGeorge B. Dantzig: “How LinearProgramming First Began,” and JohnDennis, Chairman of the MathematicalProgramming Society: “An EssentialTool for Decision Support.”

During the opening session the Beale-Orchard-Hays, Dantzig, Fulkersonand Tucker prizes were awarded orannounced. The jury reports and thenames of the prize winners can befound on the following pages.

The Sixteenth International Symposium on Mathematical

Programming, August 24-29, 1997, was hosted by École

Polytechnique Fédérale de Lausanne (EPFL). Tom Liebling,

Dominique de Werra and their team made a great effort to

organize a symposium of supreme quality that was also the

biggest one ever. Despite the size of the meeting, the organization

ran as smoothly as for a small workshop. We thank them all!

A F a n t a s t i c

SYMPOSIUM !

Left to right:Dominique de Werra,George B. Dantzig andTom Liebling at theopening session inthe concert hall.

O P T I M A 5 5 PAGE 2OCTOBER 1997

The 1997 Beale-Orchard-Hays Prize

The Beale-Orchard-Hays Prize is dedicated to the memory ofMartin Beale and William Orchard-Hays, two pioneers in com-putational mathematical programming.

The Beale-Orchard-Hays Prize honors a paper or book on com-putational mathematical programming. There are three criteriathat are important in selecting the winning nomination:

1. The magnitude of the contribution to the advancement ofcomputational and experimental mathematical programming.

2. The originality of the ideas and methods.

3. The clarity and excellence of the exposition.

For the 1997 award, the work must have appeared in the openliterature within the years 1993 through 1996.

After reviewing many excellent nominations, the prize commit-tee decided to award the 1997 prize to Steven Dirkse (pictured,left) and Michael Ferris (right) for their paper: “The PATHSolver: A Nonmonotone Stabilization Scheme for MixedComplementarity Problems” which appeared in the journal“Optimization Methods and Software” in 1995.

In their paper the authors propose a pivoting-based Newton’smethod for the mixed complementarity problem, a problemwhich is important since it includes several problems such assolving the KKT conditions for nonconvex nonlinear program-ming, finding equilibria of games both with linear and nonlin-ear structure, and solving variational inequalities. In extensivecomputational testing, the solver described in the paper domi-nates every other recent code in efficiency. It is also very robust.Furthermore, the authors have been instrumental in collectingthe first comprehensive test set for this important class of prob-lems. They have made this test set, called MCPLIB, as well asvarious algorithms, available for comparative testing at the Uni-versity of Wisconsin.–ACHIM BACHEM,KARLA HOFFMAN,PHILIPPE TOINT,ROBERT J. VANDERBEI (CHAIR)

P R I Z E S

Clyde Monma (L) and LesTrotter, previous and cur-rent Society treasurers.

A FANTASTIC SYMPOSIUM!

The scientific program consisted of 446 parallel sessions divided over 25different topics. Twenty-five semiplenary lectures were presented. The numberof participants was the biggest ever: 2268 people from 63 countries. Thefollowing special sessions were organized:

Anthony V. Fiacco’s 70th Birthday

Philip Wolfe’s 70th Birthday

The Pivot Choice Challenge, with Love to George

Tucker Prize Session

Steven Vajda Memorial Session

The Mystical Power of Twoness: In Memoriam Eugene L. Lawler.

Equally well taken care of was the social program. On Tuesday evening, August26, a Simplex Birthday Party was organized. The Master of Ceremonies was DickCottle, and speeches were given by Bob Bixby, Hans Kuenzi, Tom Magnanti, andPhil Wolfe. All these addresses are included in OPTIMA, beginning on Page 4.Wednesday evening featured a cruise and banquet on Lac Léman. The Collège deCuivres de Suisse Romande provided beautiful musical intermezzi.

O P T I M A 5 5 PAGE 3OCTOBER1997

The 1997 Dantzig Prize

The George B. Dantzig Prize isjointly administered by the Math-ematical Programming Society andthe Society for Industrial and Ap-plied Mathematics. This prize isawarded to one or more individualsfor original research which, by virtueof its originality, breadth and depth,is having a major impact on the fieldof mathematical programming. Thecontributions eligible for consider-ation must be publicly available and

may address any aspect of mathemati-cal programming in its broadestsense.

The 1997 George B. Dantzig Prizewas jointly awarded to RogerFletcher and Stephen M. Robinson“for sustained, fundamental, and illu-minating contributions to the area ofmathematical programming rangingfrom stability theory and sensitivityanalysis to broad algorithmic develop-ments in nonlinear programming.”

Roger Fletcher and Stephen M. Robinson are congratulated by Ellis Johnson (R).

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The D. Ray Fulkerson Prize

The D. Ray Fulkerson Prize in Dis-crete Mathematics was awarded atthe opening session of the XVI In-ternational Symposium on Math-ematical Programming held inLausanne, Switzerland.

The committee for the 1997 prizeconsisted of Ron Graham, RaviKannan, and Éva Tardos (chair).To be eligible, papers had to bepublished in a recognized journalduring the six calendar years pre-ceding the year of the Symposium.The term discrete mathematics is in-tended to include graph theory, net-works, mathematical programming,applied combinatorics, and relatedsubjects. While research in these ar-eas is usually not far removed frompractical applications, the judgingof papers is based on their math-ematical quality and significance.

The 1997 Fulkerson prize was awarded to Jeong

Han Kim, for the paper The Ramsey Number

R(3,t) Has Order of Magnitude tt

2

log , which ap-

peared in Random Structures and Algorithms vol 7

issue 3, 1995, pages 173-207.

The Ramsey number R(s,t) is the minimum n such

that every red-blue coloring of the edges of the

complete graph Kn includes either a red complete

graph on s nodes or a blue complete graph on t

nodes. The Ramsey number was introduced by

Erdös and Szekeres in a paper in 1935. The 1947

paper by Erdös on the symmetric Ramsey number

R(t,t) is generally viewed as the start of the proba-

bilistic method in combinatorics. Since then de-

velopments in bounds on the Ramsey number

have been intertwined with developments of the

probabilistic method.

After the symmetric case, the Ramsey number

R(3,t) is the most studied. Erdös and Szekeres

proved that R(3,t) is O(t2), this upper bound was

improved by Graver and Yackel in 1968 to

O t tt

2 log loglog( ), and then in 1990 by Ajtai, Komlòs,

and Szemerédi to Ot

t

2

log( ). The best known lower

bound for R(3,t) was Wt

t

2

2log( ) due to a 1961 pa-

per by Erdös.

Jeong Han Kim’s paper solves this 60-year-old

problem by improving the Erdös lower bound to

match the upper bound of Ajtai,

Komlós, and Szemerédi. The

paper is a veritable cornucopia

of modern techniques in the

probabilistic method; it uses mar-

tingales in a sophisticated way to

obtain strong large deviation

bounds.

Justification: It is the committee’sunanimous judgment that the broad,sustained, and fundamental works ofRoger Fletcher and Steve Robinsondeserve the Dantzig Prize. One can-not consider the nonlinear part ofmathematical programming withoutwondering why they have not alreadybeen recognized.

Roger Fletcher has made fundamentalalgorithmic contributions to almostall areas of nonlinear optimization.He is well-known for his contribu-tions to the development of nonlinearconjugate gradient and variable-met-ric methods for unconstrained opti-mization, but his contributions havealso had a profound impact on non-linear least squares and nonlinearlyconstrained optimization. His influ-ence on the development of optimiza-tion and its impact on applications isdeep and far-reaching.

Steve Robinson’s work has funda-mentally affected the analysis of thesolution, stability, and sensitivity ofnonlinear optimization problems. Inparticular, he introduced generalizedequations and the strong-regularitycondition into optimization. Hiswork has had a major impact in theanalysis and development of algo-rithms for systems of nonlinear equa-tions, nonlinear complementarity,variational inequalities, andnonlinearly constrained optimiza-tion.

Not only is their contribution im-portant, but its sustained nature con-tinues to impress us.

–CLOVIS C. GONZAGA,

ELLIS L. JOHNSON (CHAIR),

CLAUDE L. LEMARÉCHAL,

JORGE J. MORÉ

O P T I M A 5 5 PAGE 4OCTOBER 1997

C O M M E N T SO NT H E

Master of CeremoniesRichard W. Cottle’s Speech“As you know, tonight we are here to celebratethe 50th birthday of the Simplex Method. It’s thetype of thing that some people call The Big Five-Oh. Sometimes it is an occasion to take stock andthink about the half century that’s passed andperhaps the half that might be coming. In anyevent, these have been fifty incredibly productiveand happy years despite the appearance of certainupstarts [interior point methods] now in theirteens.

One might ask what the future holds in store forthe Simplex Method – will there be a mid-life cri-sis? Who knows? Here is a somewhat pessimistic

thought from the English poet, T.S.Eliot. He said ‘The years between fifty

and seventy are the hardest. Youare always being asked to do

things and are not yet decrepitenough to turn themdown.’ Well, being in thatage bracket, I can attest tothe truth of that state-

ment. However, Ithink there is amuch more optimis-tic way of looking atthings, and that is

what we are here to dotonight.

Some twenty-one years ago atthe Symposium in Budapest,

Jack Edmonds gave me this littlepin. It’s a likeness of a polytope,

and with a little generosity, youcould think of it as a simplex – I’m

sure Jack did. On this simplex is writtenNON STOP MAGIC. I think we’ve got amagical method that we’ve been benefitingfrom for a long time, and I prefer to thinkthat this magic will continue to be herein a non-stop way. Certainly the inspir-

David Karger

James Geelen

The 1997 Tucker Prize

The jury examined 21 sub-mitted papers. The ’97 vin-tage is abundant, diversifiedand of high quality. It coversmany fields of MathematicalProgramming and gives en-couraging evidence of the vi-tality of the Society.

The choice of three finalistswas difficult. The jury solic-ited the advice of some re-nowned specialists. We wouldlike to thank them for theiranonymous but highly appre-ciated contributions. As oneof them put it, “Phew, it wastough.”

The three finalists are DavidKarger, James Geelen, andLuis Vicente.

The winner is David Karger.His thesis on “Random sam-pling in graph optimizationproblems” is at the crossroadsof computer science and opti-mization. Karger showed thatapplying random sampling totraditional network optimiza-tion leads to surprisinglysimple algorithms whose run-ning times are asymptoticallyfaster than previously knownalgorithms for these problems.In particular, he gives a lineartime algorithm for computinga minimum cost spanning treeand an O(n2) algorithm forcomputing a global minimumcut. The jury found the con-tribution deep, original andelegant.

The second laureate is JamesGeelen for his work on“Matchings, matroids andunimodular matrices.” In histhesis James Geelen general-izes the idea of unimodularmatrices to square matrices,focusing on the principal mi-nors. Just as matrices andtheir minors link withmatroids, square matrices andtheir principal minors link

with objects known as “Delta-matroids.” Geelen obtained anice generalization of results ofCamion on uniquerepresentability and of Tutteon excluded minors. Some ofhis proof techniques have al-ready been applied with successto solve other difficult prob-lems.

Our third laureate is LuisVicente. His work entitled“Trust-region interior-pointalgorithms for a class of nonlin-ear programming problems”pertains to the domain of con-tinuous optimization. Bydrawing on the most efficientknown techniques such assequential quadratic program-ming, trust regions and interiorpoint algorithm, Luis Vicenteproposes and analyzes newefficient methods to solvedifficult nonlinear program-ming problems, in particular,those arising in the area ofoptimal control.

–KURT ANSTREICHER,

RAINER BURKARD,

JORGE NOCEDAL,

JEAN-PHILIPPE VIAL (CHAIR),

DAVID WILLIAMSON

P R I Z E S

Luis Vicente

O P T I M A 5 5 PAGE 5OCTOBER1997

S I M P L E X

OF THE

OC

CA

SI

ON

ing example set by its inventor, GeorgeDantzig, gives a lot of support to thispoint of view.

Now I’d like to tell you what we have instore for the presentations this evening.We’ll have four speakers, the first of

whom I’ll introduce in a moment. Once thesetalks are over, I think we should all participate ina nice singing of a certainsong, and you may feelfree to use the SimplexMethod’s first name inthis.

So let me call forward thefirst of our speakers thisevening. This is H.P.Kuenzi. I’d like to say justa word or two about him.For those of you who arenot so acquainted with thescene here in Switzerland, he is a very importantfigure due in part to his early involvement inmathematical programming and operations re-search generally. He is a coauthor of a very well-known book on nonlinear programming. It was,for example – as I understand it – the first Ger-man language book on the subject ever pub-lished. He was a founder and a driving force inthe formation of the Swiss OR Society, and youare probably aware of the fact that he subse-quently had a career in politics and affairs ofstate. It is a great pleasure for me to introduce toyou H.P. Kuenzi.”

Hans Kuenzi’s Speech“It is a great honor for our country that the im-portant and high-level International Symposiumon Mathematical Programming is held in Swit-zerland at the EPFL. We are very happy that wehave the unique opportunity to discuss with morethan 1400 scientists from 62 different countriesthe large field of mathematical programming,which developed immensely during the past

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years. As president of the Support Committee ofour Symposium I have also the honor to welcomeyou to Lausanne in the French-speaking part ofSwitzerland.

Ladies and gentlemen, before I turned to politics(as a member of the government of the CantonZürich), I was professor of Mathematics of Op-erations Research at the University of Zürich. In

this double function as politician andmathematician I am very glad abouttwo important events: As a Swiss politi-cian I am glad that the constitution ofour state can celebrate its 150th birth-day. As a mathematician Iam also glad that we cancelebrate the 50th SimplexBirthday Party at this ex-clusive Symposium.

At this occasion I remem-ber the times when we in

Switzerland began to study newmethods for linear programming. Imyself received a grant in 1958 fromthe Swiss national science founda-tion, which gave me the opportu-nity, as a young professor, to studythe new field of operations researchin the USA. There I had the grandopportunity to meet you, GeorgeDantzig, at the Rand Corporation inSanta Monica, and I recall the inter-esting discussions with you about thetheory and applications of linear programming inseveral domains, especially in economics. At thesame time I became acquainted with PhilipWolfe whose works, especially on the theory ofnonlinear programming, I appreciated verymuch.

When I returned to Switzerland, I gave my firstcourses in linear programming in Zürich andstarted writing my first book in German, also onLinear Programming, together with ProfessorWillhelm Krelle from the University of St Gallen.It was the first book on this topic that appeared

B I R T H D A YP A R T Y

in Switzerland. The reason this book was sopopular among the students was surely the sym-pathetic ‘Introductory Remarks of George B.Dantzig,’ which he began with the words, ‘In thebrief span of one decade from its conception in1947, in connection with the planning activities ofthe military, linear programming has come intowide use in industry. In academic circles, mathema-ticians and economists have written books on thesubject. Interestingly enough, in spite of its wide ap-plicability to everyday problems, linear program-ming was unknown except for isolated exampleswithout influence before 1947...’ I am sure thatthis first book stimulated many students in Swit-

zerland to study this interesting algorithm.

In the beginning of the sixties several chairs inoperation research and computer science werecreated where, within the field of applied math-ematics, the theory and practice of mathematicalprogramming and the simplex algorithm weretreated more and more.

Dear George Dantzig, with these short greetings Ihope to have convinced you that, thanks to you,linear programming and the simplex methodcame to Switzerland. I thank you forty years laterfor this, and I am happy to be able to celebrate

O P T I M A 5 5 PAGE 6OCTOBER 1997

the 50th birthday of the Simplex Algorithm,whose father you are, together with you here.

As a little birthday gift I again give you the littlebook, written 40 years ago, entitled Linear Pro-gramming, with introductory remarks fromGeorge B. Dantzig, where you finally wrote, ‘Thispaper is an introduction for German speaking read-ers to the basic ideas of linear programming and inparticular to the simplex method. It is with greatpleasure that I recommend this book to those inter-ested in the subject.

September 11, 1958 George B. Dantzig, The RandCorporation, Santa Monica, California’”

Cottle:“It’s been suggested by a number of people that Ihave some jokes ready for this occasion, but asyou see, there is no audio-visual equipment here,and I wouldn’t be able to identify those jokeswith slides that would tell you they’re jokes; soI’m going to skip that and move along to the nextspeaker, who will be Phil Wolfe.

Phil Wolfe began his career at Princeton aftergraduating from Berkeley. He was there for awhile and then joined the RAND Corporationwhere he worked in the field of mathematicalprogramming for many years, developing anenormous number of ideas from which we allhave derived great benefit. I’m happy to say thatI’ve known him since 1961 and regard him as agood friend. It’s a pleasure to introduce him toyou now.”

Phil Wolfe’s Speech(The editor has kindly allowed me to expand onthe remarks I made at the banquet. What followsis what I would have said were it not that ban-quet diners, unlike readers, cannot skip para-graphs.)

“I was delighted at being invited to speak in cel-ebration of the simplex method, since I owe themajor part of my career to it. I hope that it willbe heard as tribute to the simplex method and,even more, to George Dantzig and others whocontributed so much to it.

In yesterday’s plenary session George spoke of theexcitement he and his colleagues felt about theirwork in the Air Force’s Project SCOOP in theforties. While Washington was the best place tobe, you didn’t have to be there to share in thatexcitement, as I found.

The birth year of the simplex method was alsothat of the second edition of Theory of Games andEconomic Behavior by von Neumann andMorgenstern. As a second-year graduate studentin mathematics at Berkeley in the Fall of 1949,planning to work in the foundations of math-ematics, I was unaware of both. My reading thenincluded not only Hilbert and Ackerman’sMathematische Logik but Astounding Science Fic-tion Magazine. The October 1949 issue of thelatter (price $0.25) changed my career. A shortstory, ‘The Finan-Seer’ by E.L. Locke, told how agroup of university professors rescued theirschool’s failing finances by using somethingcalled Game Theory to beat the stock market.Entranced, I got the book the story cited andstarted trying to understand this new kind of ap-plication of mathematics. Converted, I found aBerkeley professor, Edward Barankin, willing toguide work in that area.

While not a fan of game theory, Ed was seriousabout the application of mathematics to indus-trial problems and had personal connections withPrinceton University, with the Rand Corpora-tion, with the Management Science ResearchProject at U.C.L.A., and with former Berkeleystudent George Dantzig. He had me read dozensof reports from those friends. I learned somethingof the simplex method and of the broad range ofimportant problems that it and related techniquesmight address.

When I was looking for a job for the summer of1951, Ed turned to George, and I was invited towork with Project SCOOP in Washington! Hispeople were full of the excitement he spoke of.On arriving I visited each to learn about thework. One, after shaking my hand, said, ‘My jobis to make a detailed model of the Americaneconomy. You’ll have to excuse me now, I’m ter-ribly busy.’ Others – George and Alex Orden es-pecially – had time for me; and so have they in allthe years afterward.

The work of SCOOP had attracted so much at-tention that the Air Force and the Bureau ofStandards held the ‘Symposium on Linear In-equalities and Programming’ that June (whichmuch later we designated the First Symposiumon Mathematical Programming). There, at myfirst scientific meeting, I was thrilled to see peopleI had known only through their writings: GeorgeForsythe, Theodore Motzkin, Albert Tucker.

At that time the possibility that degeneracy mightmake the simplex method fail was of concern.

Alan Hoffman, at the Bu-reau of Standards, hadjust created the celebratedproblem on which themethod did indeed fail. George asked me tostudy the issue, although he had really resolved italready; a report by his student, Edmonston,showed that sufficiently small perturbations inthe data of a problem would let the simplexmethod work. I found that the perturbationscould be recast as a “lexicographic” ordering ofthe data. That, or perhaps just that word, takenfrom my German reading, was the contributionof my first technical paper.

Returning to Berkeley I split my time betweenthe management science studies Barankin en-couraged and my self-chosen thesis topic, atheory of games with no stop rule, in which eachplayer would make an infinite sequence of moves.Barankin didn’t like my subject much and judgedit adequate only when a paper by David Gale andF.M. Stewart appeared on the same subject butwith fewer results than I already had. Still, hewanted it to be only part of my dissertation andhad me include the lexicography work as theother. Actually, neither games nor programs got alot of respect at Berkeley then. A fellow graduatestudent wanted me to explain linear program-ming. ‘You mean you are trying to find a certainvertex of a polyhedron,’ he asked, ‘and there areonly finitely many vertices?’ I answered, ‘That’sright.’ ‘But that’s trivial!’ he declared. That re-mark was easier to ignore than one by GriffithEvans, Chairman of the department, normallykindly, whose distinction awed us all. Toward theend of my thesis defense he said, ‘This is all verywell, Mr. Wolfe, but where is the mathematics?’

With Barankin’s aid the defense succeeded. Heperformed one more invaluable service, helpingme get an instructorship at Princeton University,where I arrived in the Fall of 1954. That was justwhen Albert Tucker, department chairman,needed an eager young man to run errands, teachcalculus, and participate in his ONR LogisticsResearch Project, which had supported such lu-minaries as Shapley, Gale, and Kuhn. (Neither Alnor I could have guessed that a life-long friend-ship would begin there. Forty years later I told Alhow a story in Astounding Science Fiction gotme into game theory, and he told me that the au-thor learned about it from a popular lecture ofAl’s. I find that wonderful.)

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O P T I M A 5 5 PAGE 7OCTOBER1997

Marguerite Frank was another member of the Lo-gistics Project. Together we developed the basicidea of the ‘Frank-Wolfe’ algorithm, tying itclosely (and probably unnecessarily) to the find-ing of Barankin and Robert Dorfman at Berkeley,that the solution of a convex quadratic program-ming problem is a ‘complementary’ extremepoint solution in an appropriate simplex tableau.We submitted this work, naturally, to the NavalResearch Logistics Quarterly. At the same timeHarry Markowitz, at The Rand Corporation, hadwritten his seminal paper modeling the portfolioproblem and solving it as a parametric quadraticprogramming problem and sent it to the Quar-terly. Our buddy Alan Hoffman was the editor,and economically sent our paper to Harry for ref-ereeing, and his to me. Years later Harry and Iconfessed to each other that we had not really un-derstood what we read, but felt it important, andapproved it. They appeared back to back in theMarch-June, 1956 issue. I then determined tounderstand Harry’s algebra. I didn’t, but foundthat it could be modelled as basis changes in thesimplex method. That suggested an algorithmthat actually used the simplex method in theBarankin-Dorfman tableau with a special deviceto ensure complementarity. I wrote that up as ‘Asimplex method for quadratic programming’early in 1957 and rushed a copy to George, whohad joined the Rand Corporation. His letter ofJanuary, 1957, said, ‘Assuming validity of yourproof, I am very much impressed...’ It was valid,and I joined Rand in June, 1957.

It was hoped that I could replace Bill Orchard-Hays, who had just left Rand after writing a pro-duction simplex method routine for the IBM704. Leola Cutler was able to adapt that code toquadratic programming, and the observation thatonly six instructions needed changing was greatadvertising–if you ignored the fact that you hadto massively rearrange the punched-card inputdata. I became quite skilled at wiring the card re-producing machine. However, I found Bill’s as-sembly language routine impenetrable and pio-neered the use of FORTRAN at Rand, to theamusement of its professional programmers.With Leola’s help the resulting simplex methodpackage proved more effective than some in as-sembly language and, owing to the modular de-sign the higher level language facilitated, highlyflexible. It served as a vehicle for testing manycomputational variants of the simplex methodand as a subroutine in other procedures. The lat-ter aspect brought to Rand two visitors of great

importance in my later life: Michel Balinski, forwhom we programmed his new procedure forfinding all the vertices of a polyhedron, andRalph Gomory, who wanted it for his work ininteger programming.

I could go on for hours about the excitement ofworking at Rand at that time amidst its stellarcast (and not even mention the sun-drenchedbeach a block away). Most important for mewere Ray Fulkerson and, of course, George. I’vebeen called a student of George’s. I never was inthe formal sense, but as a colleague I certainlystudied his work and his methods. One result ofcareful attention to his attacks on several differ-ent large-scale linear programming problems wasthe realization that they had a common idea thatcould be formalized as what we called ‘the de-composition principle.’ That concept turned outto have great appeal – it made sense in specialtiesranging from computer science to economics. Ihave been gratified ever since in the linkage ofmy name to George’s in that work (and onlymildly vexed at seeing a recent translation fromRussian refer to ‘Dantzig-Hulf’).

Most of my work at Rand, until Gomory luredme to the IBM Research Center in 1966, wasspent in testing and trying to improve variants ofthe simplex method; teaching the simplexmethod (UCLA and USC); extending the sim-plex method (the reduced gradient method); andusing the simplex method practically (for ex-ample, to prescribe a minimum-cost diet everyweek for some California dairy herds). I evenused some of the simplex method in a procedureI proposed for the solution of a system of nonlin-ear equations, a generalization of the secantmethod. It seemed good in practice and I triedhard to establish its convergence in general, andcouldn’t; indeed, a colleague showed later that itcould blow up on nice-looking problems. Un-known to me, a distinguished predecessor pro-posed the method a long time ago. He wrote,‘The study of its convergence presents some diffi-culties.’ I learned this from Ortega’s book onnonlinear equations, where he writes of ‘themethod of Gauss and Wolfe.’

I must stop here, although I never stopped cel-ebrating the simplex method: using it, teachingit, even defending it against the hilariously mis-understood threat of the ellipsoid algorithm (OP-TIMA No. 1, June, 1980). I think I’ve saidenough to justify declaring gratefully, HappyBirthday, Simplex Method!”

Cottle:“The next speaker will be Tom Magnanti fromMIT. It’s difficult to summarize all the accom-plishments that Tom has racked up over theyears. He’s been president of this and that, editorof this and that — Operations Research, for ex-ample. At MIT he is a professor at the SloanSchool as well as the Department of ComputerScience. He is member of the National Academyof Engineering. I’m delighted to say he is agraduate of my department at Stanford. In addi-tion to that, he was of course a prize student ofGeorge Dantzig. It’s a pleasure to welcome himto address you this evening.”

Thomas L. Magnanti’s Speech“Thank you Dick. As I was sitting at the dinnertable, I had an idea. I don’t know if GeorgeDantzig is up to this or not; I didn’t ask himabout it. But, it strikes me that in keeping withthe celebration this evening, each of us shouldhave a personal toast with George, and as we dothis we could contribute $10 to the Dantzig Prizeso we cannot only all jointly celebrate withGeorge but also collect money for this importantprize. We’ll see if George is up to 1,400 toaststhis evening! I think he’s still pretty robust andprobably can do it. (At this point, GeorgeDantzig interrupts.) George just said he’d preferto just contribute the money himself and forgetabout the toasts.

It is difficult to followour previous speakerswho have so muchhistory of workingwith George Dantzig.Let me share one briefstory with you, andthen I’d like to dosomething a little bitdifferent for this evening. The story goes backabout 20 years, when George was visiting MITand I had a few less gray hairs. On that occasionwe were traveling in my car, which had very poorshocks, through some terrible roads, lined withone pothole after another, in Cambridge, Massa-chusetts. Sitting in the back seat of the car wereGeorge Dantzig, Bob Dorfman, and Saul Gass.As we would drive down the street, about everyten feet we’d hit a bump, jolting them all - in-deed, it would seem that at each pothole one ofthem would rise and hit his head on the top of

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O P T I M A 5 5 PAGE 8OCTOBER 1997

the car. We finally arrived safely at our destina-tion. Later my wife Beverly said, ‘You could haveset back the history of linear programming com-pletely by driving around Cambridge with thesegentlemen; you could have killed them all off inthis one evening.’

Some of you may think that the Simplex Methodoriginated with George Dantzig, projectSCOOP, and the Rand Corporation. But actu-ally the Simplex Method started in New England.It originated late in the last century. There’s acorporation in New England called the SimplexWire and Cable Company. I don’t know if youever heard of this company. It used to have a fa-cility right next to MIT. They’re the companythat installed the first transatlantic undergroundtelephone cable. They developed the SimplexMethod for putting cable underground. So Ithink that we must address a priority issue here aswe undertake our celebration.

In graduate school, all of us develop keen friend-ships with our fellow students, who generally arethe same age as us. In many cases, we developlife-long relationships with these individuals.Now I had the occasion of meeting a certain indi-vidual, about my age, a year before I enrolled ingraduate school and this individual and I actuallyhad one of these rare occurrences when we trav-eled from undergraduate to graduate school to-gether. Occasionally, we get to meet the parentsof the students who we study with and we de-velop lifelong relationships with them as well.Now my newfound friend was called Simplex. Ihad encountered this friend through a book thatSaul Gass had written. My friend and I traveledto Stanford University to study. And what I’dlike to do this evening is in honor of my friendSimplex’s birthday, and as we sometimes do atbirthday parties, to recall some of the events ofthe day when my friend was born. Hopefully, thisrecollection will put this 50th birthday celebra-tion in some perspective: by reflecting on some ofthe events of 1947, we might be able to attainsome sense of how historic it is to have a friend(method) who’s reached such a ripe old age.

Some Events in 1947Monumental Events

• India and Pakistan become independent.

• Hungary becomes a Soviet satellite. Romaniabecomes a Communist state.

• At the Harvard commencement exercises June5, U.S. Secretary of State George C. Marshall

proposes the Marshall Plan to give financial aidto European countries ‘willing to assist in thetask of recovery.’ Congress authorized some$12 billion in the next 4 years.

• President Truman asked Congress to aidGreece and Turkey to combat Communist ter-rorism March 12. Congress approves theTruman Doctrine on May 15.

• United Nations Security Council voted unani-mously April 2 to place under U.S. trusteeshipthe Pacific islands formerly mandated to Japan.

Social and Economic Events

• The U.S. Congress passes Taft-Hartley Act,over President Truman’s veto, to curb strikes.

• The major world powers sign the GeneralAgreement on Tariffs and Trade (GATT) tosignificantly lower tariff barriers, end some tar-iff discrimination, and help revitalize worldtrade.

• On April 11, Jackie Robinson and the Brook-lyn Dodgers break the color barrier in majorleague baseball.

• Levittown, nearly identical prefab housing,goes up on Long Island to meet the boomingpost World War II housing demand.

• Ronald Reagan becomes President-yes he does!Of the Screen Actors Guild.

• Minute Maid Corporation has its beginningsas the Vacuum Foods Company (more on or-ange juice later!).

• Sony Corporation begins as the Tokyo Tele-communications Company.

• Hollywood black list of alleged communistsympathizers compiled.

• Paris couturier Christian Dior introduces the‘New Look’ design.

Scientific Inventions/Products

• Transistor.

• Long Playing Records.

• B.F. Goodrich introduces the first tubeless au-tomobile tires.

• Reddi-Wip, Inc., introduces Reddi-Wip, thefirst major U.S. aerosol food product. FounderMarcus Lipsky advertises aerated ‘real’whipped cream inpressurized cans.

• Colgate-Palmolive-Peet introduces Ajaxcleanser.

• The Raytheon Company introduces the firstcommercial microwave oven.

• MSG (monosodium glutamate) is producedcommercially for the first time.

• Almond Joy was introduced to augment thepopular Mounds bar.

• Variable pitchpropeller.

• The PolaroidLand Cameradevelops its ownfilms within itsbody - in 60 seconds.

• Subatomic particle pion.

• Willard Frank Libby discovers the atomic timeclock (carbon 14 dating).

• Joshua Lederberg and Edward Lawrie Tatumfind that sexual reproduction occurs in bacteria- leads to the field, bacterial genetics.

• OR pioneer and British physics Nobel Laure-ate Patrick Maynard Stuart Blackett advancesthe theory that ‘all massive rotating bodies aremagnetic.’ (He has previously worked on cos-mic rays and especially on the electrical par-ticles known as ‘mesons.’)

• Flying a U.S. Bell X-1 rocket plane, U.S. AirForce captain Chuck Yeager breaks the soundbarrier.

The Arts

• Tennessee Williams’ A Streetcar Named Desirewins the Pulitzer Prize as does W.H. Auden’s,The Age of Anxiety.

• Albert Camus publishes The Plague.

• Thomas Mann publishes Doctor Faustus.

Born• Tom Clancy• Stephen King• David Mamet• Salman Rushdie• Kareem-Abdul Jabbar• Johnny Bench• Dick Fosbury (of the Fosbury Flop)• Nolan Ryan• Elton John• Farrah Fawcett• Arnold Schwarzenegger (counterpoint to

Farrah Fawcett?)• Steven Spielberg• Hillary Rodham Clinton• Dan Quayle (Republican offset to Hillary

Rodham Clinton?)• O. J. Simpson

And, one other very important thing happened in1947: A young fellow by the name of GeorgeDantzig develops a mathematical model calledlinear programming. He discovers a clevermethod of solution, my friend Simplex.

I hope that looking back upon the events of theday in 1947 gives all of us some sense of the his-toric nature of your birthday, Simplex. As welook back upon these scientific discoveries, the

S I M P L E X

O P T I M A 5 5 PAGE 9OCTOBER1997

important economic events of the day, and theimportant artistic achievements of the day, Ithink that the Simplex Method stands shoulderto shoulder against any of those accomplishments- in terms of its intellectual and scientific contri-bution, its economic contribution, and perhaps,most importantly for all of us, its artistry. Thankyou very much.”

Cottle:“To round out this quartet of speakers we haveBob Bixby, professor at Rice University, alsoknown as Mr. CPLEX, the man who gave us thebag — or we could say the bag man, I’m notsure. He’s going to reflect on the past and, I be-lieve, also on the future of linear programmingand the simplex method. Ladies and gentlemen,here is Bob Bixby.”

Bob Bixby’s Speech“I thank the organizers very much for this invita-tion. It’s a great honor.

It was trying to think howto start. One of myfriends suggestedsomething, and I de-cided it was not abad idea. He sug-gested I start out by

saying, ‘The SimplexMethod: she hasbeen veery, veerygood to me.’

Indeed, it’s true.All of us here owe a

great deal to the Simplex Method. I among all ofus probably owe the most. I’m simply thankfulthat George hasn’t asked me to pay up!

I decided that I would say just a few short wordsabout the development of computation in theSimplex Method. I will try to keep it short. I havea stack of about 200 slides over there in case any-body wants to hear more.

So, as I was preparing this talk – of course, I wantto emphasize that I was not around when theearly codes on linear programming were beingwritten, so – I had to ask people!

If you go back to about 1952, ’53, the very firstcodes were being written at The Rand Corpora-tion by Orchard-Hays in collaboration withGeorge Dantzig. In those days they could solve,

after a couple of years of work, problems on cardprogrammable computers, problems with abouttwenty-six constraints. And ‘solve’ you have totake with a grain of salt. It took them eight hoursto solve one such problem, and somebody had tobe standing there feeding the cards through themachine. That was 1953.

You get into the sixties, ’62 through the mid six-ties, and the first commercially successful codeswere being developed. That is what John Tomlintold me: LP90 and LP94, which ran on IBM7090, 7094 computers. These codes could solveproblems with up to one thousand rows. Ofcourse, there was a small problem as I understandit. These machines had ten tape drives on them.Now, as I say, I wasn’t around, so I don’t reallyknow what a tape drive is, but I can imagine. Ap-parently a problem took eleven tape drives to ac-tually run, so somebody had to stand there.

I also talked to Milt Gutterman who, many ofyou may know, was an important figure in thedevelopment of computer codes for linear pro-gramming in the late sixties, early seventies, andbeyond. He related to me a story from when hestarted his first real job – in about 1960. Hewalked in the door, as a freshly trained OR ana-lyst, and there was somebody standing withstacks of cards, picking them up, walking a fewsteps and putting them down, waiting, pickingthem up, walking a few steps, putting themdown, ... And he asked this young man what hewas doing. He said ‘solving a linear program.’

So it was a big step from there to the early 1970sand the first real codes, ones that could be usedon a wide variety of problems. It was actuallyquite a remarkable collection of codes that weredeveloped in the late sixties and early seventies,culminating with the development of a codecalled MPS3 with Whizard, which originally waswritten by Dennis Rarick, John Tomlin, JimWelsh, with a number of other people makingimportant contributions. That code, which wasbased upon super sparsity, an idea that emergedaround 1971, is still, to this day in my opinion,quite a good code. The problem is that it waswritten in the tradition of the day. It was writtenfor a specific machine. It was written in machinelanguage. It was not flexible.

Those codes: MPS3, MPS3 with Whizard,MPSX, MPSX/370 and a number of other codesbrought us into the eighties. The early eighties iswhen I started to get into the subject. Up to thatpoint, I had been working on something called

matroids – which are not related to hemorrhoids!How many of you know what matroids are?(Comment – a show of a few hands.)

When I first learned about linear programming in1965, of course, we worked with those thingscalled tableaus, and I liked them so much that be-tween 1965 and 1982, I couldn’t face a linearprogram. But right about then, in the early eight-ies, personal computers came out and I was luckyenough to be at Northwestern University, to-gether with a fellow named Bob Fourer, who hadbeen at Stanford where all this activity in linearprogramming was going on. The pilot modelshad been developed there, and Bob just knew alot about the practice of linear programming. Iknew nothing about it.

Fourer showed up at Northwestern and pro-ceeded to painstakingly inform me about howone should really write a linear programmingcode. And then Tom Baker, a good friend ofmine who started Chesapeake Decision Sciences,proceeded to prod me for two years to take thiscode that I had started writing and develop it fur-ther.

So I got started in linear programming in theearly eighties, and it was a perfect time to getstarted. Integer programming was flowering. Ma-chines were becoming available in which memorywas essentially unlimited. Really, if you look backat the codes that were available before, if they hadhad unlimited memory, they could have beenwritten to be as good as those we have today.

That brings me to 1984, a very exciting time.That was when Karmarkar published his work. Itseemed like competition was in the air, with newand larger problems constantly being solved. I re-member working on a problem together with IrvLustig, John Gregory, Dave Shanno, and RoyMarsten. The problem arose from airline crewscheduling and had 837 rows and some 13 mil-lion columns. It would have been unimaginablejust a few years before to solve, even the LP madeup of the first 30,000 columns of that model, andwe solved the full LP in about 6 minutes using aspecial-purpose simplex method. Today we cansolve that model on a workstation in about twoand a half minutes using standard LP tools.

I am very much involved in research on the Trav-eling Salesman Problem, a problem that serves asa good indication of what is being done in integerprogramming these days. And integer program-ming, in my opinion, is the place where the sim-

S I M P L E X

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O P T I M A 5 5 PAGE 10OCTOBER 1997

plex method has found its home. We are solvingproblems in which we solve sequences of thou-sands of linear programming problems, each ofthem having on the order of fifteen thousand con-straints, thirty thousand variables, and three orfour hundred thousand nonzeros, and we don’tthink even a minute about it. We just let it run.

By the way, something we have Don Goldfarb tothank for is the Dual Steepest Edge Algorithm,which has really carried the Simplex Method for-ward into this generation.

There are numerous new applications of linearprogramming that lie ahead of us. We’ve all seenthe explosion in the airline industry. That’s noth-ing compared to what we’re about to see in sup-ply-chain optimization, and in other, as yet undis-covered, areas of application.

Finally, I would just like to close with a remarkthat I am going to attribute to John Forrest. Hemade it at the end of a talk a few years ago, inwhich, after putting up a bunch of tables, he said,‘So, we see that the Simplex Method is ten timesfaster than the Simplex Method.’”

S I M P L E X

ORIGINAL PHOTOGRAPHS BY A. HERZOG.

HYBRID PHOTO ILUSTRATIONS BY E. DRAKE.

Mathematical Programming’s CoverSeveral colleagues asked me about the origin of the now familiar cover

design of Mathematical Programming at the 16th Symposium in

Lausanne. The story is simple though.

There were a number of technical points to negotiate with our pub-

lisher when the journal was launched in 1971 on the basis of the pool

of papers presented at the 7th Symposium held in the Hague in 1970.

Among these were the cover, the density (or number of words per

page), and others. I dealt with these, the Society having only come into

existence some time after the journal.

North-Holland’s dictum was clear: simple, one color, though two tones

of the one color would be acceptable. I felt two features needed to be

pictured: extreme point and separation. Indeed, the attractive logo of

the Lausanne Symposium elicits similar ideas. I toyed with drawings

myself but soon realized that angles aesthetic to the eyes are not triviali-

ties, so a professional hand was needed. I posed the problem to an out-

standing architect (and an old and dear friend) Philetus Holt of

Princeton, NJ. He solved it and graciously gave it to me for the cover.

- MICHEL BALINSKI

O P T I M A 5 5 PAGE 11OCTOBER1997

The Mathematical Programming Society isin fine fettle. Our treasury is plush, thejournal continues in the forefront and thebacklogs are manageable. We have justelected an outstanding slate of officers.The meeting in Lausanne was the largest

ever, the organization was superb, the talks were great, thelake cruise was beautiful, the weather was nice, and the hotelprices were not as high as some of our members feared theymight be. Tom Liebling and his committee did a wonderfuljob. I think special thanks are in order for the polite andhelpful young people in the information T-shirts. The chal-lenge is there for Georgia Tech, host of the 2000 meeting,to meet.

By MPS tradition, the 2000 meeting will be in NorthAmerica. As you know, our society does not have a confer-ence staff, and our meetings are organized and held at theuniversity that submits the most compelling proposal. Thismeans that we count on the local organizers to make ourmeeting work. This is one reason why I am very excitedabout having a meeting at GaTech. This major internationalcenter for mathematical programming, operations research,and systems engineering is one of the premier US engineer-ing schools. GaTech has some fine new facilities as a resultof the recent Olympic Games held in Atlanta, and Atlanta isa beautiful city with interesting restaurants in every pricerange.

You know by now that the Councils of both organizationshave approved a contract for SIAM to provide the MPSmembership services we were previously paying ISI (Interna-tional Statistical Institute) to provide. In choosing a pro-vider, we were limited for practical reasons to other profes-sional organizations large enough to have a permanent staff.The only serious candidates were INFORMS and SIAM.The bids were similar, and both were more attractive thanour existing arrangement. Our choice of SIAM was influ-enced by their outstanding use of the Internet in deliveringmember services and by the consideration that there wouldbe less of a perception that MPS was being “taken over” by alarger society –INFORMS – with which it has so manycommon interests.

Some of you have told me that fear of “takeover” makes youuneasy about this change, but all agree that a change fromthe current arrangement was needed and that the concernabout a takeover would have been greater had we hired IN-FORMS instead of SIAM. I appreciate your expressions ofconcern since it demonstrates the loyalty that we all feel forMPS, with its informal (but committed) volunteer gover-nance, its single-minded emphasis on research, and itsstrong international flavor. We have no intention of becom-ing a SIAM “Activity Group” for Math Programming; nordoes SIAM have any interest in blurring the distinction be-tween our two societies. We on the Council and ExecutiveCommittee simply feel that the professional staff of SIAMcan handle our member services more ably than the available

Chair’s Column

John Dennisalternatives. Our firm intention is that you will see a differ-ence only in better service. Some noticeable changes that weexpect to see include an up-to-date address list, accessibleand updateable through the Web.

There is more change afoot; we are now seeking bids for anew journal publisher. Our goals are to make an agreementthat will halve our library subscription price, to keep thejournal free to our members, to increase the Society’s shareof subscription revenues, and to keep abreast of develop-ments in electronic publishing as an alternate or additionaldistribution system. Several members have told us of rescu-ing our journal from their library “cut” list where it wasplaced because of the high library subscription price. Thereis no reason why we should tolerate being out of line in oursubscription price. I have named an ad hoc committee ofSteve Wright, Jan Karel Lenstra, and Bob Bixby to study theissues and recommend a new publisher. SIAM, INFORMS,Wiley, and Springer have all submitted preliminary bids.The current publisher also submitted a bid but, unlike theother bidders, they have expressed reluctance to lower thesubscription price.

The MPS owns the title and MPS logo/cover art and thecopyright of all but the first volume, so though the formatwill certainly change to have less of that expensive whiteempty space, Math Programming A&B will still be recog-nizable to its loyal readers, and we will keep the same edito-rial systems in place. As an aside, you will enjoy MichelBalinski’s article in this issue on how the cover art came tobe. Also, I really enjoyed Richard Cottle’s talk in the PhilWolfe birthday session in which he solved the “MPS Prob-lem” he derived from the MPS logo.

I felt at this symposium that we have been around longenough now to have a proud history. Tony Fiacco, AlanHoffman, Phil Wolfe, and, of course, George Dantzig, wereactive at the symposium. I only wish, as I am sure many ofyou do, that Garth McCormick had been there and thatMartin Beale could have been there. I want my students tohave the experience that I had as a young researcher; I wasinspired by the presence at meetings of the “legends.”

Finally, I want to end this column with a tribute to JanKarel Lenstra and Don Hearn. Don is Mr. OPTIMA. Hehas given years of valuable service to making OPTIMA afine newsletter. Karen Aardal will become editor and Don,who is taking on administrative duties at the University ofFlorida, will continue as publisher. Jan Karel is Mr. MPS.He embodies all the values that make ours such a fine soci-ety, and he is the repository of a vital store of knowledge ofthe Society. He is unselfish in his devotion to MPS, and hegives great advice. I owe him more than I can possibly sayhere. Jan Karel, Clyde Monma, and Steve Wright were cru-cial in the big decisions we have made, and they and Chair-Elect Jean Phillipe Vial will be counted on for the big oneswe will make. Thanks, Jan Karel, and do not think we aregoing to stop trying to take advantage of all you have to of-fer just because your term has ended.

O P T I M A 5 5 PAGE 12OCTOBER 1997

At the business meeting in Lausanne, JohnDennis (Chairman), Jan Karel Lenstra (Vice-Chairman), and Steve Wright (Chairman,Executive Committee) reported on thefollowing items:

Lausanne Symposium

Election results

Editors, Mathematical ProgrammingSeries A and B, and OPTIMA

Change of membership administrationfrom ISI to SIAM

Location of next international symposium

Location of IPCO meetings in ’98 and ’99

Suggested revision of the constitution.

The Chairman-Elect Jean-Philippe Vial alsohad the opportunity to address the members atthe business meeting.

Lausanne Symposium

The Lausanne Symposium was a huge success!The Chairman of the Local Organizing Com-mittee, Thomas Liebling, reported on thenumber of sessions and participants and somefinancial aspects of the meeting. Tom and thewhole Lausanne team received an enthusiasticapplause for their fantastic effort.

The 1997 election results, as announced on July3, 1997, are as follows:

Chairman-Elect: Jean-Philippe Vial (Switzer-land)

Treasurer: Clyde Monma (USA)

Council Members-at-Large: Karen Aardal (TheNetherlands), Kurt Anstreicher (USA), DavidShmoys (USA), Uwe Zimmermann (Germany)

Jean-Philippe Vial will act as Vice-Chairmanuntil August 1998 when he will become Chair-man. In August 1998 our current ChairmanJohn Dennis will become Vice-Chairman, a po-sition that he will keep until the Symposium inyear 2000.

Editors

Don Goldfarb and John Birge will continue aseditors of Mathematical Programming A and Brespectively. Don Hearn will end his term aseditor of OPTIMA and will act as “publisher.”Karen Aardal will replace Don as editor. DonHearn is the founding editor of OPTIMA andhas acted as editor since the start in 1980. Hiswork has been very much appreciated by themembers, and he was thanked with warm ap-plause by everyone at the meeting.

SIAM to handle MPS member services

Membership services for the Mathematical Pro-gramming Society will be handled by the Soci-ety for Industrial and Applied Mathematics(SIAM), effective January 1, 1998, upon termi-nation of the current contract with the Interna-tional Statistical Institute (ISI). The agreementwith SIAM was approved by MPS Council inDecember, 1996.

Under the terms of the agreement, SIAM willhandle traditional membership services such asmaintenance of the membership address list,provision of the address list to the publishers ofMathematical Programming and OPTIMA, an-nual distribution of the list to MPS members,and annual membership renewal. SIAM person-nel will also handle routine queries about mem-bership, address changes, and missed copies ofthe journal.

The agreement also enhances the services cur-rently provided by ISI in a number of ways. Theonline, searchable membership list (currentlymaintained on an informal basis by SteveWright) will be integrated with the official MPSmembership list and maintained professionallyby SIAM. MPS members will appear in theCombined Membership Listing for the Math-ematical Sciences, alongside members of SIAM,MAA, and other societies. (MPS members canpurchase the Listing by checking a box on their

N E W SF R O M T H E C O U N C I L

annual renewal.) Reminder notices for member-ship renewal will now be sent up to five times,in contrast to the current single notice. Mem-bership can be renewed quickly and conve-niently through the World-Wide Web.

In approving the new agreement with SIAM,the MPS Council took into account the excel-lent level of service provided by SIAM to itsown members, the quality of the SIAM Website, and the attractive financial terms of theagreement. The many MPS members who arealso members of SIAM are familiar with thehigh standards of this organization and themany shared interests of the two societies. Welook forward to a productive relationship in theyears ahead.

Location of next International Symposium

The International Symposium on MathematicalProgramming in year 2000 will be hosted byGeorgia Institute of Technology. GeorgeNemhauser and Martin Savelsbergh will sharethe responsibility of the organization. We wishthem the best of luck and look forward to At-lanta 2000!

Location of IPCO meetings in 1998 and 1999

The 1998 IPCO meeting will be held in Hous-ton. Andy Boyd will be chairing the Local Orga-nizing Committee, and Bob Bixby will be theChairman of the Program Committee. The1999 meeting will be held in Graz with ReinerBurkard as Local Chair and Gerard Cornuéjolsas Program Chair.

Suggested Revision of the Constitution

A few revisions to the Constitution of the Math-ematical Programming Society were suggested.The suggestions were approved at the businessmeeting. The current Constitution is printed infull on the following page.

O P T I M A 5 5 PAGE 13OCTOBER1997

I. NameThe society is an internationalorganization to be called‘Mathematical ProgrammingSociety’. It will henceforth, inthese statutes, be referred to asthe Society.

II. ObjectivesIts objectives are thecommunication of knowledge ofthe theory, applications, andcomputational aspects ofmathematical programming andrelated areas and the stimulationof their development. In order torealize these objectives, theSociety publishes a journal, holdsInternational Symposia andsponsors such other activitiesconsistent with the objectives asmay be directed by the Council.

III. MembershipThe membership of the Societyconsists of individual membersand of corporate members.Individual members as well ascorporate members join theSociety by application in a formprescribed by the Council.

IV. Council1. The elected members of theCouncil of the Society are theChairman, the Vice-Chairman,the Treasurer, and four at-largemembers. The Editors-in-chief ofthe journal and the Chairman ofthe Executive Committee shall beinvited to all Council meetingsand shall be included on allCouncil correspondence. All mustbe members of the Society.

2. The Chairman chairs themeetings of the Council. TheCouncil votes by majority of theelected members present, withthe Chairman having a castingvote.

3. The Chairman will submit areport on the activities of theSociety when he relinquishes hisoffice, and his report will bepublished in the journal or in anewsletter of the Society. He willchair a business meeting on theoccasion of any InternationalSymposium held during his termof office.

4. The Vice-Chairman replacesthe Chairman whenever thenecessity arises.

5. The Treasurer is responsiblefor the administration of the fundsof the Society, as directed by theCouncil. The Treasurer shallmake a financial report to theSociety at the InternationalSymposium held within his termof office.

financial obligations betweenthe Society and the organizingcommittee.

3. In the following section onelections the word ‘term’ isdefined to be the period fromthe end of the business meetingheld during the InternationalSymposium to the end of thebusiness meeting of thefollowing InternationalSymposium.

VI. Elections1. Elections for the Offices ofChairman, Treasurer and thefour at-large members of Councilare held four months prior toeach International Symposium.The elected Chairman serves onCouncil for the two termsfollowing his election. He is theChairman from one year afterthe beginning of his first termuntil one year after thebeginning of his second term. Hetakes the office of Vice-Chairmanduring the remainder of hisperiod of service. The Treasurertakes office one year after thebeginning of the term followinghis election and he serves untilone year after the beginning ofthe next term. At-large membersof Council serve for the termfollowing their election. If theoffice of Chairman becomesvacant, it is filled automaticallyby the Vice-Chairman. TheChairman, after consultationwith Council, may appoint amember of the Society to fill anyother office that becomes vacantuntil the next election. No onemay serve for more than twoconsecutive terms as an electedat-large member of Council.

2. The Chairman invitesnominations for all elections,giving at least two months noticethrough the journal of theSociety of the closing date forthe receipt of nominations.Candidates must be members ofthe Society. They may beproposed either by Council orby any six members of theSociety. No nomination that is inaccordance with the constitutionmay be refused, provided thatthe candidate agrees to stand.The Chairman decides the formof the ballot.

VII. Secretariat1. The Council is assisted by aSecretariat, which is supervisedby the Chairman of theExecutive Committee andTreasurer.

2. The Secretariat will keep anup-to-date list of members of theSociety, and a list of past andpresent members of the Council,with an indication of theirfunctions.

VIII. FeesThe membership fee is fixed byCouncil, and may differ forindividual and for corporatemembers. A member who hasnot paid his dues before the endof the current year will bedeemed to have left the Society.

IX. JournalThe Journal is distributed free ofany charge addition to themembership fee to all membersof the Society, to their lastknown address.

X. AgentsCouncil may approve thepayments of membership fees,or of subscription fees for thejournal, in national currency, tolocal agents in countries where itis difficult for individual membersto obtain convertible currency.

XI. Other activitiesIn addition to InternationalSymposia, the Society maysponsor conferences andseminars. The organization ofsuch sponsored meetings issubject to directives by theChairman of the Society.

XII. Amendment of the Con-stitutionIf proposed by at least ten of themembership of the Society, or byvote of the Council theconstitution may be amended bya majority of voters, either at abusiness meeting of the societyon the occasion of anInternational Symposium, or bya written ballot. Proposals mustreach the Vice-Chairman at leasttwo months before the votingtakes place.

XIII. Bylaws1. In order to carry out theobligation as set forth in thisconstitution and to conduct thebusiness of the Society, theCouncil shall adopt bylaws. Thebylaws may be adopted,annulled, or amended by anaffirmative vote of at least fourmembers of the Council. TheCouncil shall have the authorityto interpret the bylaws.

2. Council shall pass bylawsgoverning elections designed topromote and maintaininternational representation ofthe Council and ExecutiveCommittee.

Constitution of the Mathematical Programming SocietyAdopted 27 July 1978 Adopted in revised form 29 August 1997

6. The Editors-in-chief of thejournal are appointed by theCouncil subject to the terms ofthe contract in force withpublishers of the journal. Theyare responsible for implementingthe directives of the Council, inthe organization of the journal,and for carrying out its policy.

7. At each InternationalSymposium there will be ameeting of the outgoing Counciland of the incoming Council.These meetings may becombined at the discretion of theChairman. An additionalmeeting must be held at therequest of at least threemembers of the Council. Theplace of such a meeting isdecided by the Chairman. TheChairman makes arrangementsfor the taking of minutes atmeetings of the Council andbusiness meetings of the Society.

8. The policies of the Council arecarried out by the ExecutiveCommittee. The Chairman of theExecutive Committee isnominated by the Chairman ofthe Society and is appointed bythe Council. He is responsible forexecuting the executivedirectives of the Council, foradvising the Council, and fororganizing the ExecutiveCommittee. The Chairman of theSociety and the Treasurer are exofficio members of the ExecutiveCommittee. The Chairman of theExecutive Committee mayappoint additional members withthe concurrence of the Chairmanof the Society.

9. The Council appoints suchother committees as it findsnecessary to carry out thebusiness of the Society or tofurther its objectives. TheChairman of the Society and theChairman of the ExecutiveCommittee are ex officiomembers of all such committees.

V. International Symposia1. International Symposia aresponsored by the Society atintervals of between 24 and 48months. The Chairman of theSociety nominates and theCouncil elects the Chairman forthe organization of the nextInternational Symposium.

2. Fees for the InternationalSymposium are fixed by thelocal organizing committee, inconsultation with the Chairmanof the Society. The Council shalladopt guidelines regarding the

PAGE 14

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WHEN YOU USE THE COLORSYNC 2.0 CMS, YOU CANNOT SEPARATE BITMAPEDIMAGES INTO PANTONE HEXACHROME COLORS. (APPLE COLORSYNC 2.0 DOES NOTSUPPORT HIGH-FIDELITY COLOR.) THE COLORSYNC 2.0 CONTROL PANEL DEVICE,EXTENSION, AND MONITOR PROFILES ARE AVAILABLE FROM APPLE COMPUTER ANDON THE WORLD WIDE WEB AT THE FOLLOWING LOCATION: FTP://FTP.INFO.APPLE.COM/ YOU CAN OBTAIN ADDITIONAL PROFILES FROM APPLE OR THEMANUFACTURER, OR YOU CAN CREATE CUSTOM PROFILES USING THIRD-PARTYTOOLS. PS FILES USING TIFF IMAGES EMBEDDED WITH OPI COMMENTS ARE NOWIMPORTED WITH CORRECT BOUNDING BOX INFORMATION AND PRINT CORRECTLYTO POSTSCRIPT DEVICES. RGB-TO-CMYK CONVERSIONS NOW CLOSELY MATCHTHOSE OF ADOBE ILLUSTRATOR 6.0. THE CREATE ADOBE PDF PREFERENCES FILE

STORES PREFERENCES FOR THE LAST FOUR PUBLICATIONS YOU PROCESSED, AS WELL

AS GLOBAL SETTINGS FOR ANY OTHER PUBLICATIONS. TO CHANGE THE DEFAULT

GLOBAL SETTINGS, FOLLOW THESE STEPS: THE MICROSOFT OLE FILES INSTALLED WITH

PAGEMAKER 6.0 ARE NO LONGER REQUIRED TO START PAGEMAKER ON A POWER

MACINTOSH. HOWEVER, THE OLE FILES ARE NECESSARY IF YOU DO THE FOLLOWING:

IF YOU ENCOUNTER A MACINTOSH SYSTEM ERROR TYPE 1 OR 11, THERE ARE SEVERAL

POTENTIAL CAUSES, INCLUDING: \— “POWER MACINTOSH: TYPE 11 & NO FPU

ERRORS TECHNOTE (2/96)” AVAILABLE AT: HTTP://CGI.INFO.APPLE.COM/CGI-BIN/

READ.WAIS.DOC.PL? “TECHNOTE : UNDERSTANDING TYPE 11 & NO FPU INSTALLED

ERRORS ON THE POWER MACINTOSH” AVAILABLE WE HAVE RESEARCHED THIS

PROBLEM EXTENSIVELY AND HAVE NOT FOUND ANY SOURCE OF SYSTEM ERRORS

IN PAGEMAKER ITSELF. THE UPDATED TAGGED TEXT IMPORT FILTER REPAIRS A

NUMBER OF PROBLEMS WITH MISHANDLED FORMATTING AND A PROBLEM WITH

TEXT BEING LOST ON IMPORT IN CERTAIN CASES. THE TAGGED TEXT EXPORT FILTER

FIXES A PROBLEM IN WHICH THE ORIGINAL FILTER REPLACED SECOND AND

SUBSEQUENT PICT DATA WITH FIRST INLINE PICT DATA. THE NOTE ON PAGE 399

INCORRECTLY DESCRIBES THE TAGS REQUIRED AT THE TOP OF TEXT FILES. THE TAGS

SHOULD BE <PMTAGS 1.0 MAC> (FOR FILES CREATED ON THE MACINTOSH

PLATFORM) OR <PMTAGS 1.0 WIN> (FOR FILES CREATED ON THE WINDOWS

PLATFORM.) IN THE DESCRIPTION OF IMPORTING INLINE GRAPHICS ON PAGE 408,

THE TAG SHOULD BE <& “PATHNAME INCLUDING FILENAME”> NOTE THE ADDITION

OF A SPACE AFTER THE FIELDS AND THE USE OF QUOTATION MARKS, NOT BRACKETS.

FOR EXAMPLE: <&200 200 0 “FRESHAIR:BOATFPO.GIF”> FOR COATED STOCK AND

UNCOATED STOCK RESPECTIVELY, REPLACE THE PREVIOUS VERSIONS OF THE

IDENTICALLY-NAMED

þ Algorithms and Experiments(ALEX98) Building BridgesBetween Theory and ApplicationsTrento, ItalyFeb. 9-11, 1998

þ ICM98Berlin, GermanyAug. 18-27, 1998

þ International Conference onNonlinear Programming andVariational InequalitiesHong KongDec. 15-18, 1998

NO

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THE NICHOLSON PRIZE

1998George NicholsonStudent PaperCompetition

The INFORMS Student AffairsCommittee announces the 1998George Nicholson Competition forthis year’s best OR/MS papers writ-ten by a student. There are four con-ditions for eligibility:

1) The entrant must have been astudent on or after January 1, 1997;

2) The paper must present originalresearch results;

3) The research must have been con-ducted while the entrant was a stu-dent; and

4) The paper must be written by theentrant with only minor outsideeditorial assistance. One or moreadvisors may appear as co-authors ofa paper, but the student must be the‘first author’.

Prizes will be awarded at theINFORMS Montreal Meeting,April 26-29, 1998. Winners will beinvited to present their papers at themeeting.

Entrants should submit six (6) cop-ies of one paper comprised of nomore than 25 double-spaced pages.The entries must be accompanied bya letter signed by both a faculty ad-visor and the entrant attesting thatthe four eligibility conditions havebeen satisfied. These entries shouldbe delivered no later than January15, 1998, to the chair of the prizecommittee:

Garrett J. van RyzinGraduate School of Business412 Uris HallColumbia UniversityNew York, NY 10027212-854-4280gjv1@columbia.edu

O P T I M A 5 5 PAGE 15OCTOBER 1997

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M C MI I IX C V

nars may be organized at the initia-tive of groups of participants. En-glish, French, German, and Russianare the official languages of theCongress.

All Plenary and Invited Lectures willbe published in the Proceedings ofICM’98; after the Congress, a com-plimentary copy of these Proceed-ings will be sent to each OrdinaryMember. Abstracts of all lecturesand of all short presentations will bedistributed free of charge to Ordi-nary Members at Congress check-in.

The Fields Medals and theNevanlinna Prize will be awardedduring the Opening Ceremony onthe first day of the Congress. Thiswill take place in the InternationalCongress Center Berlin (ICC); allother scientific events will be held atTechnische Universitaet Berlin. Noscientific activities are scheduled forSunday, August 23.

In an effort to reach out to a wideraudience, the ICM’98 organizershave initiated several cultural activi-ties related to mathematics that areattractive to the general public. Inparticular, there will be aVideoMath Festival, software dem-onstrations, talks about mathematicsand its relations to other subjects,several exhibitions (Mathematics inthe Arts, etc.), and other events(Mathematics and Music, etc.).

Special consideration will be givento the impact of the Nazi regime onmathematics in Berlin and Ger-many.

Social Events: On August 18 therewill be a buffet-banquet for all regis-tered participants of ICC. Duringthe Congress, a number of guidedtours of Berlin, visits to museums,and walking tours will be offered.On Sunday, August 23, it will bepossible to choose from several ex-cursions. For that evening ticketshave been reserved for the opera,The Magic Flute, at the DeutscheOpera. Registered participants maypurchase tickets in advance for theseevents as well as for many day tripsand pre- or post-congress tours toplaces of interest in the vicinity ofBerlin.

Organization: Up-to-date informa-tion about all aspects of ICM’98 isavailable on the following website:http://elib.zib.de/ICM98. This in-

International Congress ofMathematicians

Berlin, GermanyAugust 18-27, 1998

The Organizing Committee ispleased to announce that the nextInternational Congress of Mathema-ticians will take place in Berlin, Ger-many, from Tuesday, August 18,through Thursday, August 27,1998.

It will be held under the auspices ofthe International MathematicalUnion (IMU) and sponsored bymany other institutions.

Mathematical Program

Responsibility for the scientific pro-gram lies with the Program Com-mittee appointed by IMU. Therewill be about 20 one-hour PlenaryLectures covering recent develop-ments in the major areas of math-ematics and about 170 45-minuteInvited Lectures in 19 sections. Thesections are as follows:

1. Logic2. Algebra3. Number Theory and ArithmeticAlgebraic Geometry4. Algebraic Geometry5. Differential Geometry and GlobalAnalysis6. Topology7. Lie Groups and Lie Algebras8. Analysis9. Ordinary Differential Equationsand Dynamical Systems10. Partial Differential Equations11. Mathematical Physics12. Probability and Statistics13. Combinatorics14. Mathematical Aspects of Com-puter Science15. Numerical Analysis and Scien-tific Computing16. Applications17. Control Theory and Optimiza-tion18. Teaching and Popularization ofMathematics19. History of Mathematics

Every registered participant (tradi-tionally called Ordinary Member) ofthe Congress will have the opportu-nity to give a short presentation, ei-ther during a poster session or in theform of a 15-minute lecture. A for-mal call for such presentations willbe issued in the Second Announce-ment. Informal mathematical semi-

cludes information about registra-tion, abstract submission, etc. Cor-respondence should be directed to:icm98@zib.de. It will be forwardedto an appropriate member of theOrganizing Committee. If electroniccommunication is not available, youmay also write to the ICM’98 Secre-tary Prof.Dr. J. Winkler at the ad-dress below.

Registration and Accommodation:

DER-CONGRESS, a professionalcongress and tour organizer, hasbeen appointed by the OrganizingCommittee to handle all non-scien-tific matters for individual partici-pants: registration to the Congressand the social events, hotel reserva-tions, tourist program, collection ofregistration fees, etc. The formalregistration procedure for the Con-gress will be described in the SecondAnnouncement (below).

Participants will be housed in severalhotels in Berlin; the necessary reser-vations have already been made byDER-CONGRESS. In addition,DER-CONGRESS will make stu-dent residences available and willprovide a certain number of privateaccommodations at an inexpensiverate for participants willing to acceptless comfort. Detailed informationon locations and rates will be pro-vided in the Second Announcement.

Forms for registration and accom-modation requests will be madeavailable on the ICM’98 server inJanuary 1998.

SECOND ANNOUNCEMENT

The Second Announcement ofICM’98 will describe the activitiesof the Congress in more detail andgive instructions on how to com-plete the registration process andobtain accommodations. It will pro-vide more, although not complete,information on the scientific pro-gram, contain a call for contributed

short presentations, and give in-structions regarding the submissionof abstracts.

The Second Announcement willalso include advice on how to pro-ceed upon arrival at airports andtrain stations, and it will be accom-panied by a brochure describing theday trips and tours organized byDER-CONGRESS.

Several conferences of a more spe-cialized nature are scheduled imme-diately before and after ICM’98.The Second Announcement willalso contain a list of such “satelliteconferences.”

To receive the Second Announcement,fill out the form on the ICM’98 server(http://elib.zib.de/ICM98).Alternatively, send an empty e-mail toicm98@zib.de with ‘SecondAnnouncement’ in the ‘SUBJECT’ line toreceive an e-mail form or contact theICM’98 Secretary Prof. Winkler at theaddress below.

The Second Announcement will bemailed from Berlin at the beginning of1998. Electronic Information onICM’98 at URL: http://elib.zib.de/ICM98 (with request form for SecondAnnouncement)

ICM’98 General E-mail Address:icm98@zib.de

Address for general correspon-dence:

ICM’98c/o Prof. Dr. J. WinklerTU Berlin, MA 8-2Str. des 17. Juni 135D-10623 Berlin, GermanyPhone: +49/30/314-24105Fax: +49/30/314-21604E-mail: winkler@math.tu-berlin.de

Organizing Committee President:

Prof. Dr. M. GröetschelKonrad-Zuse-Zentrum fuerInformationstechnik (ZIB)Takustrasse 7D-14195 Berlin-DahlemGermanyE-mail: groetschel@zib.de

Phone: +49/30/84185-210FAX: +49/30/84185-269Secretary: Sybille MattrischPhone: +49/30/84185-208ZIB-URL: http://www.zib.de

þ

O P T I M A 5 5 PAGE 16OCTOBER 1997

International Conference on Nonlinear Programmingand Variational Inequalities

Hong Kong

December 15-18, 1998

First Announcement

The conference aims to review and discuss recent advances and promisingresearch trends in some areas of Nonlinear Programming and VariationalInequalities.

Topics Include:

Nonlinear Complementarity Problems

Variational Inequality Problems

Nonsmooth Optimization Problems

Minimax Problems

Multi-level Optimization Problems

Structured Optimization Problems

Quadratic and Nonquadratic Methods

Invited Speakers Include:

O. Burdakov (CERFACS, France)

S. Dempe (Freiberg Univ. of Mining and Tech., Germany)

F. Facchinei (University of Roma, Italy)

S.C. Fang (North Carolina State University, USA)

M. Fukushima (Kyoto University, Japan)

L. Lasdon (University of Texas at Austin, USA)

Z.Q. Luo (McMaster University, Canada)

J.M. Martínez (University of Campinas, Brazil)

J.J. Moré (Argonne National Laboratory, USA)

S. Nash (George Mason University, USA)

J.S. Pang (Johns Hopkins University, USA)

P.P. Pardalos (University of Florida, USA)

E. Polak (University of California at Berkeley, USA)

D. Ralph (University of Melbourne, Australia)

R.T. Rockafellar (University of Washington, USA)

E. Spedicato (University of Bergamo, Italy)

K.L. Teo (Curtin University of Technology, Australia)

P. Tseng (University of Washington, USA)

R.J.B. Wets, (University of California at Davis, USA)

H. Yabe (Science University of Tokyo, Japan)

Y. Yuan (Chinese Academy of Sciences, China)

Conference Chairs:

L. Qi (University of New South Wales, Sydney, Australia), Email:l.qi@unsw.edu.au

J. Zhang (City University of Hong Kong, Hong Kong), Email:mazhang@cityu.edu.hk

Organizing Committee:

A. Fischer (Technical University of Dresden, Germany)

M. Fukushima (Kyoto University, Japan)

C. Kanzow (University of Hamburg, Germany)

J. Han (Chinese Academy of Sciences, China)

J. Sun (National University of Singapore, Singapore)

R.J.B. Wets (University of California at Davis, USA)

R. Womersley (University of New South Wales, Australia)

C. Xu (Xi’an Jiao Tong University, China)

X. Zhang (Chinese Academy of Sciences, China)

Call for PapersTitles and abstracts of contributed papers must be received by July 31,1998. The abstracts should be typed in Latex, not exceed one page, andbe sent to maopt@cityu.edu.hk by email.

Special Arrangements

Conference proceedings, special issues of some journals, tours and eco-nomical hotel accommodations will be indicated in the Second An-nouncement.

Further Information:

Email: maopt@cityu.edu.hk

Home page: http://www.cityu.edu.hk/ma/

or contact Conference Chairs.

O P T I M A 5 5 PAGE 17OCTOBER 1997

Rev

iew

sVisualization andOptimizationby Christopher V. JonesKluwer Academic PublishersDordrecht, 1996ISBN 0-7923-9672-3

Have you ever looked at a contour plot of a nonlinearfunction? Have you ever looked at the feasible regionof a 2-variable linear program? Have you ever lookedat a Gantt chart to analyze the solution to a schedulingproblem? Have you ever looked at a plot of the non-zero entries in a matrix? Have you ever seen the farthestinserting algorithm in action? Have you ever seen theLin-Kernighan edge-exchange algorithm in action?Have you ever seen Edmond’s matching algorithm inaction?

Visualization is, and rightfully so, an important toolin the toolkit of an optimizer. It helps to gain insightinto a problem, an algorithm, or a solution. The aboveexamples and many more are discussed in the new bookVisualization and Optimization by Chris Jones.

The book is not the prototypical example of a text inoperations research or mathematical programming. Itdoes not discuss a specific problem or a specific meth-

The book is divided into three parts. Part I: “A Frame-work for Visualization and Optimization.” It presentsrelevant background material from cognitive psychol-ogy, computer graphics, visual design, and other areas.Part II: “Visualization and the Modeling Life-Cycle.”It discusses how visualization has been or might pro-ductively be used to support distinct phases of themodeling life cycle. Part III: “Visualization for Opti-mization.” It focuses on how different representationformats have been or could be used to support opti-mization.

The book is a pleasure to read and contains a wealthof information, including many informative illustra-tions. Even so, it becomes clear that the area of visu-alization and optimization is still in its infancy. It hasnot yet lived up to its potential. Visualization offers anopportunity to make optimization even more enjoy-able, understandable, and accessible. It can enhance ourability to deliver optimization to students as well aspractitioners.

- M. SAVELSBERGH

odology; instead, it focuses solely on how visualizationcan be used to support building and understandingoptimization models, algorithms and their solutions.

The book takes the point of view that techniques fromvisualization, when applied appropriately, can improveour ability to solve people’s problems. The purpose ofvisualization is much the same as the purpose of op-timization: to provide insight into complex problems.Optimization uses sophisticated algorithms to uncoveroptimal solutions to complex problems. Visualizationuses carefully designed representations to help peopleunderstand complex problems. The book also issuesa warning: visualization, like optimization, can easilybe misused.

The book covers a lot of material. It presents basicbackground material from cognitive psychology andother fields relevant to visualization; it provides guid-ance for those seeking to visualize their problems,models, and algorithms; it discusses existing researchand practice on using visualization to support optimi-zation analysis; it surveys research that has appliedoptimization to creating visualizations; and it suggestsresearch directions for those interested in pursuingresearch on visualization applied to optimization.

þ

O P T I M A 5 5 PAGE 18OCTOBER 1997

Primal-Dual Interior-PointMethodsby Stephen J. WrightSIAM, Philadelphia, 1996ISBN 0-89871-382-X

Since Karmarkar’s method for linear programs ap-peared in 1984, numerous interior-point methods havebeen proposed and studied for various problems.Among others, primal-dual interior-point methodshave been harmoniously developed both in theory andin practice. Now they are known to be very efficientand powerful numerical methods for solving large scalelinear programs. This book covers both theory andpractice of primal-dual interior-point methods forlinear programs and briefly mentions their extensionsto other mathematical programs. The book is well-organized, comprehensive, and easy to read for experts,graduate students and even good undergraduate stu-dents who want to study this subject for the first time.

Chapter 1 gives an overview of this book introducingfundamental ideas and various important issues onprimal-dual interior-point methods. This chapter it-self is a nice self-contained survey on the subject.Chapters 2 and 3 serve as preliminaries and back-ground. They are devoted to the standard form linearprogram, the duality theory, the fundamental ideas ofprimal-dual interior point methods, the complexitytheory of algorithms, etc. Chapters 4, 5 and 6 are themajor theoretical part of this book. These three chap-ters present full theoretical complexity analyses of themost important primal-dual interior-point methods,i.e., potential-reduction methods, path-followingmethods and infeasible-interior-point algorithms,respectively. Chapters 7 and 9 discuss some furthertheoretical issues on primal-dual interior-point meth-ods; superlinear convergence and finite termination inChapter 7, and a homogeneous self-dual formulationof primal-dual interior-point algorithms which incor-porates a mechanism of getting infeasibility informa-tion in Chapter 9. Chapter 8 describes extensions ofprimal-dual interior-point methods from linear pro-grams to some other types of problems such as convexquadratic programs, convex programs, linear andnonlinear monotone complementarity problems, andsemidefinite programs. The last two chapters placemuch emphasis on practical aspects of primal-dual in-terior-point methods. Chapter 10 presents Mehrotra’spredictor-corrector algorithm on which many currentsoftware packages are based, and in Chapter 11 thereare some computational issues involved in efficientlyand stably solving large sparse systems of linear equa-tions for primal-dual search directions. Finally, severalsoftware packages, some of which are free and avail-able through the Internet, are listed in the appendix.

- MASAKAZU KOJIMA

Stochastic Modelsby H.C. TijmsJohn Wiley, Chichester, 1994ISBN 0-471095123-4

Stochastic Models is a modernized version of the author’sprevious book that also appeared with Wiley, under thetitle Stochastic Modeling and Analysis.

It contains four chapters:

1. Renewal Theory with Applications

2. Markov Chains: Theory and Applications

3. Markov Decision Processes and their Applications

4. Algorithmic Analysis of Queueing Models

Each chapter is concluded with a section, BibliographicNotes, and a well-sized section of References.

Chapter 1 provides the basics of renewal theory, thePoisson process and renewal reward processes. Further,it contains two larger sections on Reliability and In-ventory in which the theoretical results are applied.

Chapter 2 gives a very complete presentation of dis-crete and continuous time Markov chains and uses theapplications to illustrate the modeling aspects. It isconcluded with sections on Transient Analysis and thePhase Method.

Chapter 3 is devoted to the average reward Markovdecision processes. It treats Policy Iteration, LinearProgramming and Value Iteration. We also find aninteresting section on tailor-made policy iterationalgorithms that exploit the specific structure of theapplication of interest.

Chapter 4 starts with the more advanced queuingmodels as the ordinary M/G/1 queue, the M/G/1queue with batch arrivals and the G/G/1 queue. Afterthat it continues with a thorough and extensive algo-rithmic analysis of multi-server queues including finitecapacity models. As for most of the models treated inthis chapter, analytical results are very limited; theemphasis is on approximations, particularly for thedistribution of the waiting time.

As the titles of the chapters clearly indicate (applica-tions, algorithmic), the book is an attempt to help thereader to become an engineer in stochastic modeling.Although, as the author remarks, we all know that theonly way to become a modeler in this difficult area isby doing. This book with the many examples in the textand over a hundred interesting exercises, is an excel-lent way to start.

Each of these chapters can very well be used as the basisfor a course. The chapters are to a large extent inde-pendent. Chapter 2 can be studied without almost anyknowledge of the renewal theory in Chapter 1, andChapters 3 and 4 require only a very basic knowledgeof Markov chains. Each chapter starts with the basicmaterial which requires little background and only alimited amount of intuition but then continues withmore advanced topics which ask for a higher level ofunderstanding. Particularly, Chapter 4 is very inter-esting but not so simple.

In the preface we read that this book is more directedto students than to researchers, in contrast to the pre-vious version. I agree with that; it is definitely one ofthe best books for students who want to get acquaintedwith stochastic modeling, but it is a lot more thananother set of lecture notes.

In all four chapters we discover special topics in whichwe recognize the author’s research. We find manyimportant and useful approximations which take usone step further than analysis could. The emphasis ison applications and approximations which are usefulfor the engineer. But at the same time, these sectionsare important for researchers who are treating prob-lems for which no standard models exist.

For me that is just what makes Stochastic Models somuch more attractive than most of the books in thisarea. Therefore, I can recommend it to anyone who isinterested in Stochastic Operations Research.

- J. VAN DER WAL

PAGE 19

CREDITCARDNUMBER: EXPIRY DATE:

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MAILING ADDRESS:

TEL.NO.: TELEFAX:

E-MAIL:

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l I will pay my membership dues on receipt of your invoice.

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Mail to:The Mathematical Programming Society, Inc.c/o International Statistical Institute428 Prinses Beatrixlaan2270 AZ VoorburgThe Netherlands

Cheques or money orders should be made pay-able to The Mathematical Programming Soci-ety, Inc., in one of the currencies listed below.Dues for 1997, including subscription to thejournal Mathematical Programming, areDfl.110.00 (or $65.00 or DM100.00 or £40.00or FF330.00 or Sw.Fr.80.00).Student applications: Dues are one-half theabove rates. Have a faculty member verify yourstudent status and send application with dues toabove address.

Faculty verifying status

institution

A P P L I C AT I O N F O R M E M B E R S H I P

New Editorial Staff

At the Symposium, OPTIMA changed editorial staff. Don Hearn, who foundedOPTIMA in 1980, has been the editor since the start. He will now help the new edi-tor, Karen Aardal, with several publication aspects. The editorial structure will beslightly different from previous years. Karen will as editor continue with her previ-ous task as “Features Editor.” To get news on developments in our field, includingsoftware, and also to assist Karen in suggesting and attracting Feature articles,OPTIMA will have two “Area Editors”; Mary Beth Hribar, Rice University, for Con-tinuous Optimization, and Sebastian Ceria, Columbia University, for DiscreteOptimization. Book reviews will, of course, continue to form an important sectionof OPTIMA. The new Book Review Editor is Robert Weismantel, ZIB-Berlin. Youwill find the addresses of all editors on the last page of OPTIMA. In the next issueof OPTIMA there will be a short presentation of all of them. The new staff hopesthat the members of MPS will continue to provide OPTIMA with Feature articles,software information, conference notes, and all possible ideas and suggestions!

As the new editor of OPTIMA,I would like to extend a warmTHANK YOU to my predeces-sor Don Hearn for his fantasticjob with producing OPTIMAsince 1980. I also would like tothank the secretarial staff at theCenter for Applied Optimiza-tion at the University of Floridain Gainesville for all their assis-tance through the years. ElsaDrake at Gator EngineeringPublication Services has givenOPTIMA its distinguished pro-fessional style. Fortunately theywill all continue to help with

preparing and publishing OP-TIMA! Thanks as well to Don’swife Joyce who has spent numer-ous hours on editing and proof-reading OPTIMA. Also, manythanks to the previous associateeditors Faiz Al-Khayyal, Soft-ware and Computation Editor,and Dolf Talman, Book ReviewEditor, for all their efforts.

In the next issue of OPTIMAthere will be an interview withDon, where he tells us aboutboth his work with OPTIMAand his scientific activities.

–KAREN AARDAL

Reiner Burkard and Jan Karel Lenstra wereawarded the EURO Gold Medal at theEORU/INFORMS Meeting in Barcelona.

Next deadline is November 15, 1997.

ga

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au

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Than

k You

Don

!

FIRST CLASS MAIL

O P T I M AMATHEMATICAL PROGRAMMING SOCIETY

Center for Applied Optimization371 Weil HallPO Box 116595Gainesville FL 32611-6595 USA

UNIVERSITY OF

FLORIDA

Donald W. Hearn, FOUNDING EDITOR

Elsa Drake, DESIGNER

published by theMATHEMATICAL PROGRAMMING SOCIETY &

GATOREngineering® PUBLICATION SERVICES

UNIVERSITY OF FLORIDA

Journal contents are subject to change by the publisher.

EDITOR:Karen AardalDepartment of Computer ScienceUtrecht UniversityP.O. Box 800893508 TB UtrechtThe Netherlandse-mail: aardal@cs.ruu.nlURL: http://www.cs.ruu.nl/staff/aardal.html

AREA EDITOR, CONTINUOUS OPTIMIZATION:Mary Elizabeth HribarCenter for Research on Parallel ComputationRice University6100 Main Street - MS 134Houston, TX 77005-1892USAe-mail: marybeth@caam.rice.eduURL: http://www.caam.rice.edu/~marybeth/

AREA EDITOR, DISCRETE OPTIMIZATION:Sebastian Ceria417 Uris HallGraduate School of BusinessColumbia UniversityNew York, NY 10027-7004USAe-mail: sebas@cumparsita.gsb.columbia.eduURL: http://www.columbia.edu/~sc244/

BOOK REVIEW EDITOR:Robert WeismantelKonrad-Zuse-Zentrum für Informationstechnik (ZIB)Takustrasse 7D-14195 Berlin-DahlemGermanye-mail: weismantel@zib.de