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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.)

Algebraic rules for quadratic regularization of Newton's method

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Author(s):
Karas, Elizabeth W. [1] ; Santos, Sandra A. [2] ; Svaiter, Benar F. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 60, n. 2, p. 343-376, MAR 2015.
Web of Science Citations: 7
Abstract

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)

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