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