Lecture 24: Linear Programming and Two-Person Games

Description

This lecture focuses on several topics that are specific parts of optimization. These include linear programming (LP), the max-flow min-cut theorem, two-person zero-sum games, and duality.

Summary

Linear program: Minimize cost subject to \(Ax = b\) and \(x\geq 0\) 
Inequalities make the problem piecewise linear.
Simplex method reduces cost from corner point to corner point.
Dual linear program is a maximization: Max = Min!
Game: \(X\) chooses rows of payoff matrix, \(Y\) chooses columns.

Related sections in textbook: VI.2–VI.3

Instructor: Prof. Gilbert Strang