Finance Notes_Part_39

Finance Notes_Part_39 - Limit of feasible poll centers...

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Unformatted text preview: Limit of feasible poll centers Theorem Let x be the limit of unsuccessful feasible poll centers { x F k } on meshes that get infinitely fine. If f is Lipschitz near x , then f ( x,v ) for all v T H ( x ) . Corollary In addition, if f is strictly differentiable near x , and if is regular near x , then f ( x,v ) for all v T ( x ) , i.e., x is a KKT point for min x f ( x ) . Audet and Vicente (SIOPT 2008) Optimization under general constraints 89/109 Limit of infeasible poll centers Theorem Let x X be the limit of unsuccessful infeasible poll centers { x I k } on meshes that get infinitely fine. If h is Lipschitz near x , then h ( x,v ) for all v T H X ( x ) . Audet and Vicente (SIOPT 2008) Optimization under general constraints 90/109 Limit of infeasible poll centers Theorem Let x X be the limit of unsuccessful infeasible poll centers { x I k } on meshes that get infinitely fine. If h is Lipschitz near...
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This document was uploaded on 10/30/2011 for the course FIN 3403 at University of Florida.

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Finance Notes_Part_39 - Limit of feasible poll centers...

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