L18 - CO350 Linear Programming Chapter 7: The Two-Phase...

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Unformatted text preview: CO350 Linear Programming Chapter 7: The Two-Phase Method 13th June 2005 Chapter 7: The Two-Phase Method 1 Recap In the past week and a half, we learned the simplex method and its relation with duality . By now, you should know how to solve an LP problem given an initial feasible basis; give a proof of optimality/unboundedness from the final tableau; compute/read a dual optimal solution from an optimal tableau; relate dual optimal solution with shadow prices in the case of nondegeneracy. Chapter 7: The Two-Phase Method 2 Motivation Consider the LP ( P ) max c T x s.t. Ax = b x We have assumed that a feasible basis is always given. But in practice, it is usually not easy to spot a feasible basis. Duality theory says: optimal solutions to ( P ) and its dual are solutions to Ax = b, x A T y c c T x- b T y = 0 So, finding feasible solution is as hard as solving L P. Two-phase method: an algorithm that solves ( P ) in two phases, where in Phase 1, we solve an auxiliary LP problem to either get a feasible basis or conclude that ( P ) is infeasible. in Phase 2, we solve ( P ) starting from the feasible basis found in Phase 1....
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L18 - CO350 Linear Programming Chapter 7: The Two-Phase...

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