Incorporating minimum Frobenius norm models in direct search

• Author(s): Custódio, Ana Luísa ; Rocha, Humberto ; Vicente, Luís Nunes
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11216
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Derivative-free optimization; Minimum Frobenius norm models; Direct search; Generalized pattern search; Search step; Data profiles
• Document Type: Preprint
• Language: English

Description

The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a direct-search run to build the models. The minimization of the models within a trust region provides an enhanced search step. Our numerical results show that such a procedure can lead to a significant improvement of direct search for smooth, piecewise smooth, and stochastic and nonstochastic noisy problems. FCT POCI/MAT/59442/2004, PTDC/MAT/64838/2006.