Incorporating Minimum Frobenius Norm Models in Direct Search

Published: 2008/10/24

Optimization Software Benchmark, Unconstrained Optimization data profiles, derivative-free optimization, direct search, generalized pattern search, minimum frobenius norm models, search step Short URL: https://optimization-online.org/?p=10571

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.

Incorporating Minimum Frobenius Norm Models in Direct Search

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