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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 Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization

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Author(s):
Birgin, E. G. [1] ; Martinez, J. M. [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 73, n. 3, p. 707-753, JUL 2019.
Web of Science Citations: 2
Abstract

A Newton-like method for unconstrained minimization is introduced in the present work. While the computer work per iteration of the best-known implementations may need several factorizations or may use rather expensive matrix decompositions, the proposed method uses a single cheap factorization per iteration. Convergence and complexity and results, even in the case in which the subproblems' Hessians are far from being Hessians of the objective function, are presented. Moreover, when the Hessian is Lipschitz-continuous, the proposed method enjoys O(epsilon-3/2) evaluation complexity for first-order optimality and O(epsilon-3) for second-order optimality as other recently introduced Newton method for unconstrained optimization based on cubic regularization or special trust-region procedures. Fairly successful and fully reproducible numerical experiments are presented and the developed corresponding software is freely available. (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
FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
Grantee:Reinaldo Morabito Neto
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/24293-0 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support Opportunities: Research Projects - Thematic Grants