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Incorporating minimum Frobenius norm models in direct search. (English) Zbl 1190.90280
Summary: 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 noisy problems.

MSC:
90C56 Derivative-free methods and methods using generalized derivatives
90C30 Nonlinear programming
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