linear optimization lecture 1: introduction instructor: tsvetan asamov
TRANSCRIPT
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Linear Optimization
Lecture 1: IntroductionInstructor: Tsvetan Asamov
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• Elementary Linear Programming with Applications, 2nd edition by Bernard Kolman and Robert E. Beck
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Example
Need: Energy (2000 kcal), Protein (55 g), Calcium (800 mg)
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Example
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Diet Problem Formulation
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Linear Programming Examples
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Linear Programming
• Objective function
• Linear equations (equalities)
• Linear inequalities
• Linear equations and linear inequalities are referred to as linear constraints
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Standard Form
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Diet Problem
• Objective function
• Feasible solution
• Optimal solution
• Optimal value: 92.5
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Linear programming problems
• Unique optimal solution• Many optimal solutions• No optimal solutions– Infeasible problems
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Linear programming problems
• Unique optimal solution• Many optimal solutions• No optimal solutions– Infeasible problems– Unbounded problems
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Problems
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Problems
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Reading Assignment
• Review linear algebra– Vectors– Matrices– Matrix multiplication– Matrix inversion– Gauss-Jordan reduction– Linear independence and basis– Subspaces