Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization

Autor(es)

Bras, C. P. ^{[1, 2]} ; Martinez, J. M. ^[3] ; Raydan, M. ^[1]

Afiliação do(s) autor(es)

^[1] UNL, FCT, CMA, P-2829516 Caparica - Portugal

^[2] UNL, FCT, Dept Matemat, P-2829516 Caparica - Portugal

^[3] Univ Estadual Campinas, IMECC UNICAMP, Dept Appl Math, Rua Sergio Buarque Holanda, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 75, n. 1 OCT 2019.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs