MATH 5801 Linear Optimization — Lecture notes

Unit	Topics
1	introduction graphical example definition of linear programming linear inequality inference software
2	Fourier-Motzkin elimination Farkas' Lemma solving linear programming problems
3	fundamental theorem duality theory complementary slackness
4	standard form basic feasible solution tableau
5	revised simplex method cycling perturbation two-phase method
6	sensitivity analysis dual feasible tableau revised dual simplex method
7	integer linear programming cutting planes total unimodularity
8	convexity and polyhedra extreme points convex hull
9	optimization and convexity polytopes representation of polytopes
10	polyhedral cones extreme rays recession cones
11	Benders decomposition lazy constraints
12	resolution theorem Dantzig-Wolfe decomposition