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Readings

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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