Busca avançada
Ano de início
Entree
(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

A global hybrid derivative-free method for high-dimensional systems of nonlinear equations

Texto completo
Autor(es):
Begiato, Rodolfo G. [1] ; Custodio, Ana L. [2] ; Gomes-Ruggiero, Marcia A. [3]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] UTFPR, DAMAT, BR-80230901 Curitiba, PR - Brazil
[2] FCT UNL CMA, Dept Math, Campus Caparica, P-2829516 Caparica - Portugal
[3] Univ Estadual Campinas, Dept Matemat Aplicada, IMECC, BR-13083970 Campinas, SP - Brazil
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 75, n. 1, p. 93-112, JAN 2020.
Citações Web of Science: 0
Resumo

This work concerns the numerical solution of high-dimensional systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists on a matrix-free inexact Newton method that employs the Generalized Minimal Residual algorithm to solve the linear system that computes the search direction. This second phase will only take place if the first one fails to find a better point after a predefined number of reductions in the step size. In all stages, the criterion to accept a new point considers a nonmonotone decrease condition upon a merit function. Convergence results are established and the numerical performance is assessed through experiments in a set of problems collected from the literature. Both the theoretical and the experimental analysis support the feasibility of the proposed hybrid strategy. (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