Linear Optimization

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Linear Optimization

• Lecture 1 Introduction
• Instructor 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