Lecture10 - Advanced Mathematical Programming IE417 Lecture...

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Unformatted text preview: Advanced Mathematical Programming IE417 Lecture 10 Dr. Ted Ralphs IE417 Lecture 10 1 Reading for This Lecture Primary Reading Chapter 6, Sections 2-3 IE417 Lecture 10 2 Saddle Point Optimality IE417 Lecture 10 3 Lagrangian Saddle Points Recall the Lagrangian function ( x,,v ) = f ( x ) + T g ( x ) + v T h ( x ) A point ( x * , * ,v * ) with x * X, * is a saddle point for ( x,,v ) if ( x * ,,v ) ( x * , * ,v * ) ( x, * ,v * ) , x X, ( ,v ) , . IE417 Lecture 10 4 Saddle Point Optimality A point ( x * , * ,v * ) with x * X, * is a saddle point for ( x,,v ) if and only if ( x * , * ,v * ) = min { ( x, * ,v * ) : x X } g ( x * ) , h ( x * ) = 0 , and * T g ( x * ) = 0 . Furthermore, ( x * , * ,v * ) is a saddle point if and only if x * and ( * ,v * ) are the optimal solutions to P and D with no duality gap, i.e., f ( x * ) = ( * ,v * ) . IE417 Lecture 10...
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This note was uploaded on 08/06/2008 for the course IE 417 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

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Lecture10 - Advanced Mathematical Programming IE417 Lecture...

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