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Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization
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Orientador(es)
Resumo(s)
We present a new algorithm for solving large-scale unconstrained optimization problems that uses cubic models, matrix-free subspace minimization, and secant-type parameters for defining the cubic terms. We also propose and analyze a specialized trust-region strategy to minimize the cubic model on a properly chosen low-dimensional subspace, which is built at each iteration using the Lanczos process. For the convergence analysis we present, as a general framework, a model trust-region subspace algorithm with variable metric and we establish asymptotic as well as complexity convergence results. Preliminary numerical results, on some test functions and also on the well-known disk packing problem, are presented to illustrate the performance of the proposed scheme when solving large-scale problems.
Descrição
PRONEX-CNPq/FAPERJ (E-26/111.449/2010-APQ1), CEPID-Industrial Mathematics/FAPESP (Grant 2011/51305-02), FAPESP (Projects 2013/05475-7 and 2013/07375-0). Fundacao para a Ciencia e a Tecnologia- project UID/MAT/00297/2019 (CMA).
Palavras-chave
Cubic modeling Disk packing problem Lanczos method Newton-type methods Smooth unconstrained minimization Subspace minimization Trust-region strategies Control and Optimization Computational Mathematics Applied Mathematics