Duality_Theorems

Duality_Theorems - corollaries of the Weak Duality Theorem...

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ORIE 3300/5300 Fall 2011 Prof. Bland The Duality Theorem of LP (Read BHM sections 4.1-4.4) Let A be an m × n matrix, b be an m × 1 vector and c be a 1 × n vector. The LP Dual of the linear programming problem max cx ( P ) s.t. Ax b x 0 is the linear programming problem min yb ( D ) s.t. yA c y 0 . The Weak Duality Theorem of LP : If ˆ x is a feasible solution of (P) and ˆ y is a feasible solution of (D), then c ˆ x ˆ yb . In class on 11/10 we gave a short proof of this theorem. On 11/15, we will look at some
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Unformatted text preview: corollaries of the Weak Duality Theorem and we will prove The Strong Duality Theorem of Linear Programming : If (P) and (D) are both feasible, then (P) has an optimal solution x * and (D) has an optimal solution y * such that cx * = y * b ....
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This note was uploaded on 03/08/2012 for the course ORIE 3300 at Cornell.

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