Transcription of LECTURE 5: DUALITY AND SENSITIVITY ANALYSIS
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LECTURE 5: DUALITY AND SENSITIVITY ANALYSIS
LECTURE 5: DUALITY AND SENSITIVITY linear simplex methodIntroduction to dual linear program Given a constraint matrix A, right hand side vector b, andcost vector c, we have a corresponding linear programming problem: Questions:1. Can we use the same dataset of (A, b, c) to constructanother linear programming problem?2. If so, how is this new linear program relatedto the original primal problem?Guessing Ais an mby nmatrix, bis an m-vector, cis an n-vector. Can the roles of band ccan be switched?-If so, we ll have mvariables and , (1) the transpose of matrix A should be considered to accommodate rows for columns, and vise versa?(2) nonnegativevariables for freevariables?(3) equality constraints for inequalityconstraints?(4) minimizingobjective for maximizingobjective?Dual linear program Consider the following linear program Remember the original linear programExampleDual of LP in other form Symmetric pairKarmarkar sform LPHow are they related ?
Sensitivity analysis •Sensitivity is a post-optimality analysis of a linear program in which, some components of (A, b, c) may change after obtaining an optimalsolution with an optimal basis and an optimal objective value . Questions of interests:
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