Answer Happy

Dantzig-Wolfe decomposition:
When using Dantzig-Wolfe decomposition, assume the current subproblem has an op- timal solution 7 with value v. Can you give a lower bound on the optimal value of (P)? What does your lower bound become if the current dual solution (17,0) to the master problem is dual feasible?
Dantzig-Wolfe decomposition solves the linear programming problem min C s.t. Ax b X 6 X := {+ : b, E = = {x E R” : Hx = h, x > 0} = (P) Ꮖ = where X is a polyhedron and A is m x n. The procedure solves subproblems of the form min (cT – 77 A)X s.t. х E X (SP(T)) where (17,0) E Rm+1 is the current dual solution to the Master Problem.