Finance Notes_Part_13

Finance Notes_Part_13 - Convergence analysis If all...

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Unformatted text preview: Convergence analysis If all iterates belong to a bounded set, then lim inf k k = 0 . Corollary There is a convergent subsequence of iterates x k x of mesh local optimizers, on meshes that get infinitely fine. GPS methods are directional. The analysis is tied to the fixed set of directions D : f ( x k ) f ( x k + k d ) for every d D k D . Corollary If f is regular near x , then for every direction d D used infinitely often, f ( x ; d ) := lim t f ( x + td )- f ( x ) t . Audet and Vicente (SIOPT 2008) Unconstrained optimization 33/109 Convergence analysis If all iterates belong to a bounded set, then lim inf k k = 0 . Corollary There is a convergent subsequence of iterates x k x of mesh local optimizers, on meshes that get infinitely fine. GPS methods are directional. The analysis is tied to the fixed set of directions D : f ( x k ) f ( x k + k d ) for every d D k D ....
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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_13 - Convergence analysis If all...

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