Lecture20 - Advanced Mathematical Programming IE417 Lecture...

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Unformatted text preview: Advanced Mathematical Programming IE417 Lecture 20 Dr. Ted Ralphs IE417 Lecture 20 1 Reading for this lecture Sections 9.3 IE417 Lecture 20 2 Exact Penalty Functions The penalty functions ( g i ( x )) = max { ,g i ( x ) } , and ( h i ( x )) = | h i ( x ) | are called exact penalty functions . Exact penalty functions achieve optimality for a finite value of . For a convex program, must exceed the maximum of the absolute values of the optimal Lagrange multipliers. IE417 Lecture 20 3 Augmented Lagrangian Methods The problem with the foregoing penalty functions is that they are not differentiable everywhere. Idea : Shift the penalty term a little in order to reduce its dominance of the objective function. Consider the penalty function ( h i ( x )) = [ h i ( x )- i ] 2 . Assuming only equality constraints, the penalized objective function can then be written as F ( x,v ) = f ( x ) + v i h i ( x ) + [ h i ( x )] 2 IE417 Lecture 20 4 Augmented Lagrangian Methods...
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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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Lecture20 - Advanced Mathematical Programming IE417 Lecture...

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