MATH 308-3
LINEAR OPTIMIZATION
Prerequisites:
MATH 240 or MATH 232. Recommended: MACM 201.
Textbook:
Linear Programming and Its Applications by James K. Strayer, Springer, publisher.
Course Description:
Theory and applications of linear programming, geometric and computational considerations, networks, applications of duality.
Outline:
- Linear Programming
- Examples - formulation of optimization problems as linear programming.
- Problems.
- Canonical forms for linear programming problems.
- Polyhedral problems.
- Convex sets.
- The Simplex Algorithm
- Tucker Tableaus.
- The simplex algorithm for maximum tableaus.
- Minimum tableaus.
- Cycling.
- Noncanonical Linear Programming Problems
- Unconstrained variables.
- Equations as constraints.
- Duality Theory
- The dual simplex algorithm.
- Complementary slackness.
- The duality theorem.
- Application: Matrix Games
- Linear Programming formulation of matrix games.
- The von Neumann minimax theorem.
- Other applications (as time permits)
Grading Scheme
- Assignments - 15%
- Midterms - 35%
- Final Exam - 50%
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