Space Mapping: Models, Sensitivities, and Trust-Regions Methods

• Autor(a) principal: Vicente, Luís N.
• Data de Publicação: 2003
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/7749; https://doi.org/10.1023/A:1023968629245

The goal of this paper is to organize some of the mathematical and algorithmic aspects of the 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.