MATH 3801 Linear Programming — Lecture notes

Overview and prerequisite
Notation and conventions

Week Topics
1 introduction
graphical example
2 definition of linear programming
software
3 linear inequality inference
Fourier-Motzkin elimination
4 Farkas' Lemma
solving linear programming problems
fundamental theorem
5 duality theory
complementary slackness
6 standard form
basic feasible solution
tableau
7 revised simplex method
two-phase method
8 cycling
perturbation
sensitivity analysis
9 dual feasible tableau
revised dual simplex method
10 integer linear programming
cutting planes
11 introduction to convexity
extreme points
12 convex hull
polytopes
representations of polytopes