Accession Number : ADA330534

Title :   A Trust Region Framework for Managing the Use of Approximation Models in Optimization

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Alexandrov, Natalia ; Lewis, Robert M. ; Torczon, Virginia ; Dennis, J. E., Jr

PDF Url : ADA330534

Report Date : OCT 1997

Pagination or Media Count : 15

Abstract : This paper presents an analytically robust, globally convergent approach to managing the use of approximation models of various fidelity in optimization. By robust global behavior we mean the mathematical assurance that the iterates produced by the optimization algorithm, started at an arbitrary initial iterate, will converge to a stationary point or local optimizer for the original problem. The approach we present is based on the trust region idea from nonlinear programming and is shown to be provably convergent to a solution of the original high-fidelity problem. The proposed method for managing approximations in engineering optimization suggests ways to decide when the fidelity, and thus the cost of the approximations might be fruitfully increased or decreased in the course of the optimization iterations. The approach is quite general. We make no assumptions on the structure of the original problem, in particular, no assumptions of convexity and separability, and place only mild requirements on the approximations. The approximations used in the framework can be of any nature appropriate to an application; for instance, they can be represented by analyses, simulations, or simple algebraic models. This paper introduces the approach and outlines the convergence analysis.

Descriptors :   *MATHEMATICAL MODELS, *APPROXIMATION(MATHEMATICS), ALGORITHMS, OPTIMIZATION, CONVERGENCE, APPLIED MATHEMATICS, NONLINEAR PROGRAMMING.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE