Incorporating Minimum Frobenius Norm Models in Direct Search

A. L. Custódio(alcustodiofct.unl.pt)
H. Rocha(hrochamat.uc.pt)
L. N. Vicente(lnvmat.uc.pt)

Abstract: 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.

Keywords: Derivative-free optimization, minimum Frobenius norm models, direct search, generalized pattern search, search step, data profiles

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Optimization Software and Modeling Systems (Optimization Software Benchmark )

Citation: Pre-print 08-51, Dept. Mathematics, Univ. Coimbra

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Entry Submitted: 10/24/2008
Entry Accepted: 10/24/2008
Entry Last Modified: 10/24/2008

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