Accession Number:

ADA453255

Title:

Second Order Behavior of Pattern Search

Descriptive Note:

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH DEPT OF MATHEMATICS AND STATISTICS

Personal Author(s):

Report Date:

2004-01-01

Pagination or Media Count:

17.0

Abstract:

Abstract. Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on the smoothness of the objective function in a neighborhood of the limit point. Even though pattern search methods require no derivative information, we are able to prove some limited directional second-order results. Although not as strong as classical second-order necessary conditions, these results are stronger than the first order conditions that many gradient-based methods satisfy. Under fairly mild conditions, we can eliminate from consideration all strict local maximizers and an entire class of saddle points.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE