IE534_Lecture_12 - IE 534 Linear Programming Lecture 12 The Simplex Algorithm(2 Lizhi Wang Lizhi Wang([email protected] IE 534 Linear Programming 1 15

IE534_Lecture_12 - IE 534 Linear Programming Lecture 12 The...

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IE 534 Linear ProgrammingLecture 12: The Simplex Algorithm (2)Lizhi WangSeptember 19, 2012Lizhi Wang ([email protected])IE 534 Linear ProgrammingSeptember 19, 20121 / 15
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Outline1Review2Is the optimal solution always basic?3How to find a basic solution?Lizhi Wang ([email protected])IE 534 Linear ProgrammingSeptember 19, 20122 / 15
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The nuts and bolts1What exactly is a “corner point”?2Does the optimal solution always occur at a corner point?3How to find a corner point to start from?4How to check the optimality of a corner point?5How to find a better corner point if the current one is not optimal?6How to identify an infeasible or unbounded LP?7Is the Simplex algorithm guaranteed to terminate finitely?8Is the Simplex algorithm guaranteed to give the correct answer?9How efficient is the Simplex algorithm?Lizhi Wang ([email protected])IE 534 Linear ProgrammingSeptember 19, 20123 / 15
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Basic solutionA solution is a basic solution if and only if it isuniquelydeterminedby itsactiveconstraints at equality.IfAx=buniquely determines a solutionx0=Rn×1, then theremust existnlinearly independent rows inA.All rows in matrixVRk×nare linearly independent if and only ifα= 01×kis the only solution toαV= 01×n.
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