CRPC-TR98739-S						February 1998
							Revised April 1998

Title: A Rigorous Framework for Optimization of Expensive Functions by
Surrogates

Authors: Andrew J. Booker, J.E. Dennis, Jr., Paul D. Frank, David B.
Serafini, Virginia Torczon, and Michael W. Trosset

Submitted February 1998

Abstract:
The goal of the research reported here is to develop rigorous optimization
algorithms to apply to some engineering design problems for which direct
application of traditional optimization approaches is not practical. This
paper presents and analyzes a framework for generating a sequence of
approximations to the objective function and managing the use of these
approximations as surrogates for optimization. The result is to obtain
convergence to a minimizer of an expensive objective function subject to
simple constraints. The approach is widely applicable because it does not
require, or even explicitly approximate, derivatives of the objective.
Numerical resul are presented for a 31-variable helicopter rotor blade
design example and for a standard optimization test example.

Key Words: Approximation concepts, surrogate optimization, response
surfaces, pattern search methods, derivative-free optimization, design and
analysis of computer experiements (DACE), computational engineering.

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Andrew J. Booker			Paul D. Frank
booker@redwood.rt.cs.boeing.com		frank@redwood.rt.cs.boeing.com
Mathematics & Engineering Analysis
Boeing Shared Services Group

J.E. Dennis, Jr.
dennis@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

David B. Serafini
dbs@nersc.gov
National Energy Research Scientific Computing Center
E.O. Lawrence Berkeley National Laboratory

Virginia Torczon		Michael W. Trosset
va@cs.wm.edu			trosset@math.wm.edu
Department of Computer Science	Department of Mathematics
College of William & Mary