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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.)

THE USE OF QUADRATIC REGULARIZATION WITH A CUBIC DESCENT CONDITION FOR UNCONSTRAINED OPTIMIZATION

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Author(s):
Birgin, E. G. ; Martinez, J. M.
Total Authors: 2
Document type: Journal article
Source: SIAM JOURNAL ON OPTIMIZATION; v. 27, n. 2, p. 1049-1074, 2017.
Web of Science Citations: 10
Abstract

Cubic-regularization and trust-region methods with worst-case first-order complexity O (epsilon (3/2)) and worst-case second-order complexity O (epsilon (3)) have been developed in the last few years. In this paper it is proved that the same complexities are achieved by means of a quadratic-regularization method with a cubic sufficient-descent condition instead of the more usual predicted-reduction based descent. Asymptotic convergence and order of convergence results are also presented. Finally, some numerical experiments comparing the new algorithm with a well-established quadratic regularization method are shown. (AU)

FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:José Alberto Cuminato
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 14/18711-3 - Mathematical modelling systems and decisions
Grantee:José Mário Martinez Perez
Support type: Research Grants - Visiting Researcher Grant - International