Syllabus for Mathematics 640:354:
Linear Optimization

1. Definition of a Linear Programming Problem. Geometrical Solution. Extreme Point Theorem.
2. The Simplex Method. Degeneracy and Cycling. Artificial Variables.
3. Duality and the Duality Theorem. The Dual Simplex Method. Sensitivity Analysis.
4. Definition of an Integer Programming Problem. Cutting Plane Methods. Branch and Bound Methods.
5. The Transportation Problem. The Assignment Problem. Graphs and Networks: the Maximal Flow Problem, the Shortest Route Problem.