Blog for Math 340, Fall 2014
September 3: Classes start.
WE BEGIN TOPIC 1: read the supplemental article "Matrix Games and Poker"
and look at the matrix games in Washburn's book to which "Matrix Games and
Poker" refers.
September 8: How to compute the value of a 2 x 2 matrix game.
Septmeber 10: Minmax and maxmin, Alice announces versus Betty announces,
dominant strategies, irreducible games, second remarkable
theorem and the 2^(52) x 2 game, exchanging Alice and
Betty, symmetric games (their values).
September 19: Begin simplex method
September 22,24: Simplex method: pivots, basic and non-basic variables.
September 24: Shall look at
(1) an unbounded example: max x_1 + x_2 s.t., x_1 <= 6 + x_2 , x_1,x_2>=0;
(2) an infeasible example: max whatever, s.t. x_1 <= -2 , x_1>=0;
(3) a feasible example that requires two phases:
max (whatever), s.t. x_1 >= 2, x_1 <= 6, x_1,x_2>=0.
Examples (2) and (3) illustrate Chapter 2, Section 3: "Initialization."
In all examples: the simplex method should give "proofs" of correctness.
September 26: Dealing with degenerate pivots.
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LATER:
WE BEGIN TOPIC 2:
Read Chapters 1 and 2 of Vanderbei: Intro to linear programming and the
simplex method.
- Basic pivoting technique
- Initialization (when the initial dictionary is not feasible)
- Termination (Finding optimal solution or proving unboundedness)
Read Chapter 3 of Vanderbei: The Perturbation Method to avoid degenerate
pivots.
Read Chapter 4 of Vanderbei: The Efficiently of the Simplex Method
WE BEGIN TOPIC 3:
Read Chapter 5 of Vanderbei: Duality
- Duality Theory (5.1-5.4)
- Complementary Slackness (5.5)
- The Dual Simplex Method (5.6)
WE BEGIN TOPIC 4: