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Space mapping: Models, sensitivities, and trust-regions methods

Luis N. Vicente (lvicente***at***mat.uc.pt)

Abstract: The goal of this paper is to organize some of the mathematical and algorithmic aspects of the recently proposed space-mapping technique for continuous optimization with expensive function evaluations. First, we consider the mapping from the fine space to the coarse space when the models are vector-valued functions and when the space-mapping (nonlinear) least-squares residual is nonzero. We show how the sensitivities of the space mapping can be used to deal with space-mapping surrogates of the fine model. We derive a framework where it is possible to design globally convergent trust-region methods to minimize such fine-model surrogates. We consider also a different perspective of space mapping and apply it, for sake of simplicity, to the situation where the models are scalar functions. The space mapping is defined in a way where it is reasonable to assume that it is point-to-point. We prove that the surrogate model built by composition of the space mapping and the coarse model is a regular function. We also discuss trust-region methods in this context.

Keywords: space mapping, surrogate-based optimization, trust-region methods, global convergence, sensitivities

Category 1: Nonlinear Optimization

Category 2: Applications -- Science and Engineering

Citation: Preprint 01-19 Department of Mathematics, University of Coimbra, Portugal August 2001

Download: [Postscript][Compressed Postscript][PDF]

Entry Submitted: 02/11/2002
Entry Accepted: 02/11/2002
Entry Last Modified: 02/11/2002

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