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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Begiato, Rodolfo G. [1] ; Custodio, Ana L. [2] ; Gomes-Ruggiero, Marcia A. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; NOV 2019.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:Francisco Louzada Neto
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support Opportunities: Research Projects - Thematic Grants