linear optimization
DESCRIPTION
Linear Optimization. Lecture 1: Introduction Instructor: Tsvetan Asamov. Elementary Linear Programming with Applications, 2 nd edition by Bernard Kolman and Robert E. Beck. Example. Need: Energy (2000 kcal), Protein (55 g), Calcium (800 mg). Example. Diet Problem Formulation. - PowerPoint PPT PresentationTRANSCRIPT
Linear Optimization
Lecture 1: IntroductionInstructor: 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