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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).
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| WEEK # | | | | DAY 1 | | | | DAY 2 |
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| | | | | | 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 | | | | | | | | | |
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