boot if ifaf - university of illinoispublish.illinois.edu/ymb/files/2019/01/weekjan21p1.pdfna 6...
TRANSCRIPT
Basiere.sutsouoptuiuizhrs
f u IR UCR Take setEU B Csi ballof radius raround na We say that
at is a 6 if for some r o first feelsee Berta c re local aphunzer if fCnt e fca for all
if sane true for UThat of Gateaux did off at at is O
s r if it's a critical ph there are pts ad a
f al feat fca in any Brest
Weierstrgf Theorem if f is continuous on a coupactsetkThen f possesses a global duiningerCar maximizerBoot If a cunninger doesnt exist we can find Seg
of points haeen3 fCan Ifaf But by compactnessofk there is a subsequence slate f Cae riff e
see sick Then fCat f Ca for all a Ek DMaruDefinitionReminder Coupactsetsa Open cover admits finite subcoverAny sequence liesconvergentsubsequencebounded closed in 42 i coup
A function on metricspace D is called coercive iff as as 1 1 es 1 1 dist seO
origin in R somebasepointsugeireedThe If f is contineus coercive on closed mines of RhThen f has a global minimum
Drood LH E c is either empty or bounded closed
compact has a Unhium D
comp D
AppG hy polynomial PCH Etat t tan has aroot in CI
Baat If l is aerave so it allows a global inkat Z assume it o But if p Aot a.cz't a it t
Flt coefficient 0then one can find ve asVk Tao Aso real
For small u a.kz is made bigger than rest of termslaota.cz't I Kol D
TnnstwdLnmsAeotherofakoeptueohtycouohhuusiThm_Iffa.r
R is Gateaux differentiable on operaand set is a unzer then DfCoE o
Dod Taylor formula DSaeeexaupSternerpoint findpoint on the lanepuinini u sayingdisagreesto vortices of a triangle fCo7i lAolt1BoltlC0l2unoh0E.B
Solution If ItTztT i'zoo rule atoptiUmm zooA KooC B
Caveat what about this F EEuclid's optimization problem Solution
i E t E midpt between B CB C
fCa an zxE Eye hk xelConfiningpotential 9Coulombrepulsion
f win Background spectrum density forGaussian Unitary Ensemble random Herwhematrix reminder of size hxn
Rf f 4 T.mx xeTahep pu IICa nk p'Cxd TICnek see
l 7 K
Ppi nee kItf k2
I Cxe xnx e
So if Cal is unhinging picnic Tek
pCn 22kp sea o for all sea roofsoffp n Zap 2up.cz
NB Jppm e dxas
JC 4 pine ohPie Cpa seepage
ta pie Ypudx In Jpnpuke ex
por are orthogonal0 if h u