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Reformulations for nonlinear programming, second-order cone programming and semidefinite programming

Grant number: 11/23638-5
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): April 01, 2012
Effective date (End): March 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Roberto Andreani
Grantee:Ellen Hidemi Fukuda
Supervisor abroad: Masao Fukushima
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Local de pesquisa : Kyoto University, Japan  
Associated to the scholarship:10/20572-0 - Exact penalties for nonlinear optimization and second-order cone programming, BP.PD

Abstract

This work consists in developing methods to solve three well-known problems in Optimization: nonlinear programming, second-order cone programming and semidefinite programming. For each one of these problems, we consider its necessary optimality conditions and reformulate it as a system of semismooth equations. The reformulation is based on a Fischer-Burmeister-type function or a differentiable exact penalty function. Then, the generalized Newton method can be applied to this system of equations, and a merit function must be constructed in order to globalize the method. From the theoretical point of view, the method should converge globally with superlinear (or quadratic) convergence rate, and without requiring strong assumptions like the strict complementarity. In practice, under numerical experiments, the method should also be sufficiently robust and efficient. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FUKUDA, ELLEN H.; SILVA, PAULO J. S.; FUKUSHIMA, MASAO. DIFFERENTIABLE EXACT PENALTY FUNCTIONS FOR NONLINEAR SECOND-ORDER CONE PROGRAMS. SIAM JOURNAL ON OPTIMIZATION, v. 22, n. 4, p. 1607-1633, 2012. Web of Science Citations: 8.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.