Day 1

Complementary Slcakness

primary와 dual이 feasible이면, primary opimal & dual optimal iff xjzj=0 wiyi=0

Theorem 5.3.

Suppose that x = (x_1, x_2, ..., x_n) is primal feasible and that y = (y_1, y_2, ..., y_m) is dual feasible. Let (w_1, w_2, ..., w_m) denote the corresponding primal slack variables, and let (z_1, z_2, .., z_n) denote the corresponding dual slack variables. Then x and y are optimal for their respective problems if and only if

Proof

Day 2

Problem 1

Problem 2

General information

Problem 3

Transhipment problem