Finance Notes_Part_13

# Finance Notes_Part_13 - Convergence analysis If all...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## This document was uploaded on 10/30/2011 for the course FIN 3403 at University of Florida.

### Page1 / 5

Finance Notes_Part_13 - Convergence analysis If all...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online