Accession Number:

ADA455374

Title:

Generalized Pattern Searches With Derivative Information

Descriptive Note:

Corporate Author:

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

Personal Author(s):

• Abramson, Mark A.
• Audet, Charles
• Dennis, Jr, J. E.

Report Date:

2003-05-23

Pagination or Media Count:

28.0

Abstract:

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search GPS methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS poll step. Polling is done to certify the need to refine the current mesh, and it requires On function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for poll steps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the poll step to a single function evaluation. We prove that using these less expensive poll steps does not weaken the known convergence properties of the method, all of which depend only on the poll step.

Descriptors:

• *SEARCH THEORY
• ALGORITHMS
• OPTIMIZATION
• APPROXIMATION(MATHEMATICS)
• SEARCHING
• CONVERGENCE
• PATTERN RECOGNITION

Subject Categories:

• Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE