On large-scale unconstrained optimization and arbitrary regularization

Autor(es)

Martinez, J. M. ^[1] ; Santos, L. T. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, IMECC UNICAMP, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 81, n. 1 OCT 2021.
• Citações Web of Science: 0

Resumo

We present a new algorithm for large-scale unconstrained minimization that, at each iteration, minimizes, approximately, a quadratic model of the objective function plus a regularization term, not necessarily based on a norm. We prove convergence assuming only gradient continuity and complexity results assuming Lipschitz conditions. For solving the subproblems in the case of regularizations based on the 3-norm, we introduce a new method that quickly obtains the approximate solutions required by the theory. We present numerical experiments. (AU)

• Processo FAPESP: 18/24293-0 - 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