mthsc810-lecture16-1x2

# mthsc810-lecture16-1x2 - MthSc 810 Mathematical Programming...

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Unformatted text preview: MthSc 810: Mathematical Programming Lecture 16 Pietro Belotti Dept. of Mathematical Sciences Clemson University November 3, 2011 Reading for today: Sections 5.1 Reading for Nov. 8: Sections 5.2, 5.3-5.5 Homework #9 due next Tuesday Homework #10 is out! Due next Thursday. Sensitivity analysis After solving P = min { c ⊤ x : A x = b , x ≥ } , we usually have an optimal basis B and optimal primal-dual solutions x ⋆ , u ⋆ . Is B still feasible/optimal if ◮ A , b , or c change? ◮ variables/constraints are added/eliminated? Depends on primal and dual optimality: does the new problem P ′ = min { ˜c ⊤ x : ˜ A x = ˜ b , x ≥ } still have ◮ Primal feasibility: B − 1 b ≥ ? ◮ Dual feasibility: c N − c B B − 1 N ≥ ? Variable added ◮ A = ( B | N ) → ˜ A = ( ˜ B | ˜ N ) , where ... ˜ N = ( N | A n + 1 ) and ˜ B = B . ◮ ˜ c = ( c | c n + 1 ) . ◮ Unchanged b . For simplicity, let’s assume the new variable x n + 1 ≥ 0. ◮ Primal feasibility: ˜ B − 1 ˜ b = B − 1 b ≥ ? Of course. ◮ Dual feasibility: ˜ c N − ˜ c B ˜ B − 1 ˜ N ≥ ? Maybe not....
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## This note was uploaded on 03/14/2012 for the course MTHSC 810 taught by Professor Staff during the Fall '08 term at Clemson.

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mthsc810-lecture16-1x2 - MthSc 810 Mathematical Programming...

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