Lecture13 - (recession) direction of the set if • Theorem...

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IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 13- LP -Review Date: 18 November 2008 1
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Topics covered Modelling Geometric solution Requirement Space Definitions and theorems hyperplanes, basis, convexity Farka’s Lemma Simplex Duality Dual simplex Sensitivity Analysis GAMS and CPLEX 2
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Basic and Basic Feasible Solutions Take x satisfies n linearly independent rows actively and so x is a basic solution Moreover if then x is a bfs 0 1 b B x x x N B 0 1 b B 15
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Fundamental Theorem of LP Consider a. If there is a feasible solution, then there is a bfs b. If there is an optimal solution, then there is a bfs which is optimal. 0 . min x b Ax t s x c T 16
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