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Linear Optimization:
A Geometric Inquiry Course
Tien Chih
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Front Matter
Dedication
Acknowledgements
Colophon
Our goals
A note on the print version
A note on inquiry learning
1
Geometric Linear Optimization
1.1
A Brief Geometric Review of Linear Algebra
1.2
Initial Examples
1.3
Polyhedral Convextiy
1.4
Summary of Chapter 1
1.5
Problems for Chapter 1
1.5
Exercises
2
The Simplex Algorithm
2.1
Canonical Programs and the Simplex Pivot
2.1.1
A Curious Situation
2.2
The Simplex Algorithm for Canonical Maximization
2.2.1
Basic Feasible Maximization
2.2.2
Basic Infeasible Maximization
2.2.3
The Simplex Algorithm for Canonical Minimization
2.3
Cycling
2.4
Using Sage to Solve Linear Optimization Problems
2.5
Summary of Chapter 2
2.6
Problems for Chapter 2
2.6
Exercises
3
Noncanonical Problems
3.1
Unconstrained Variables
3.2
Super Constrained Bounds
3.3
Solving NonCanonical Problems with Sage
3.4
Summary of Chapter 3
3.5
Problems for Chapter 3
3.5
Exercises
4
Duality
4.1
Sensitivity Analysis
4.2
Duality Theory
4.3
Tucker Tableau’s, Pivots and Duality
4.4
Summary of Chapter 4
4.5
Problems for Chapter 4
4.5
Exercises
5
Zero-Sum Games
5.1
Min-Max Games
5.2
von Neumann Minimax Theorem
5.3
Games of Chance
5.4
Summary of Chapter 5
5.5
Problems for Chapter 5
5.5
Exercises
6
The Transportation & Assignment Problems
6.1
A Transportation problem and VAM
6.2
The Transportation Algorithm
6.2.1
Unbalanced Transportation Problems
6.3
The Assignment Problem and Hungarian Algorithm
6.4
Summary of Chapter 6
6.5
Problems for Chapter 6
6.5
Exercises
7
Network Flows
7.1
Directed Graphs and Network Flow
7.1.1
Max Flow
7.2
Max Flow - Min Cut
7.2.1
Algorithms for Max Flow and Min Cut
7.3
Weighted Graphs
7.4
Problems for Chapter 7
7.4
Exercises
8
Integer Programming
8.1
Branch and Bound Method
8.2
Cutting-Plane Method
8.3
Solving Integer Optimization Problems with Sage
8.4
Problems for Chapter 8
8.4
Exercises
9
Extra Topics
9.1
Coverings and Matchings of Graphs
9.1.1
Königs Theorem and Bipartite Graphs
9.2
Sudoku
9.3
Scheduling
9.4
Another Approach to Strong Duality
Backmatter
A
Review Material
A.1
Linear Algebra Review
A.2
Probability Theory Review
B
Simplex Pivoter
Index
Colophon
Acknowledgements
Acknowledgements
There are so many people to thank, coming soon.
