Readings

This section provides information on the assigned readings from the required textbook for the course:

Bertsimas, D., and J. N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific, 1997. ISBN: 1886529191 (see http://www.athenasc.com/linoptbook.html for more information).

Week #	Day 1	Day 2
1		Introduction; Ch. 1
2	Polyhedra; Extreme Points Sec. 2.-2.2	Degeneracy; Existence and Optimality of BFSs Sec. 2.3-2.6
3	Optimality Conditions; The Simplex Method Sec. 3.1-3.2	Simplex Method Implementations Sec. 3.2-3.3
4		Anticycling, Phase I, Complexity Sec. 3.4-3.5, 3.7
5	Duality; Proof Based on Simplex Sec. 4.7	Interpretation of Duality; Dual Simplex; Farkas Lemma Sec. 4.4-4.6
6	Separating Hyperplanes and Duality Sec. 4.7	Cones, Rays, Representation of Polyhedra Sec. 4.8-4.9
7		Sensitivity Analysis Sec. 5.1-5.2, 5.4
8	Parametric Programming; Delayed Column Generation; Cutting Planes Sec. 5.5, 6.1-6.3	Dantzig-Wolfe Decomposition Sec. 6.4
9	Interior Point Methods: Affine Scaling Sec. 9.1-9.2	Other Interior Point Methods Sec. 9.3-9.4
10	Network Problems and the Simplex Method Sec 7.1-7.3	Negative Cost Cycle Algorithm; Maximum Flow Problem Sec. 7.4-7.5
11		Duality in Networks; Shortest Path Problem Sec. 7.6, 7.9
12		Auction Algorithm Sec. 7.8
13	Integer Programming Formulations Sec. 101-10.2	Cutting Plane Methods; Branch & Bound Sec. 11.1-11.2
14	Integer Programming Duality; Lagrangean Relaxation Sec. 11.4	Integer Programming Techniques Sec. 11.3, 11.5, 11.6
15	Introduction to NP-Completeness Sec. 11.8