Algebraic rules for quadratic regularization of Newton's method

Autor(es)

Karas, Elizabeth W. ^[1] ; Santos, Sandra A. ^[2] ; Svaiter, Benar F. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Parana, Dept Math, BR-81531980 Curitiba, Parana - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Campinas, SP - Brazil

^[3] IMPA, BR-22460320 Rio De Janeiro - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 60, n. 2, p. 343-376, MAR 2015.
• Citações Web of Science: 7

Resumo

In this work we propose a class of quasi-Newton methods to minimize a twice differentiable function with Lipschitz continuous Hessian. These methods are based on the quadratic regularization of Newton's method, with algebraic explicit rules for computing the regularizing parameter. The convergence properties of this class of methods are analysed. We show that if the sequence generated by the algorithm converges then its limit point is stationary. We also establish local quadratic convergence in a neighborhood of a stationary point with positive definite Hessian. Encouraging numerical experiments are presented. (AU)

• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs