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Implementation of a software for large-scale minimization with linear constraints using trust-region methods

Grant number: 12/05725-0
Support Opportunities:Scholarships in Brazil - Master
Start date: June 01, 2012
End date: April 30, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Ernesto Julián Goldberg Birgin
Grantee:John Lenon Cardoso Gardenghi
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In the present project the development of an open software to minimize a function subject to equality and inequality linear constraints is aimed. There will be a large number of variables and constraints and, in general, the matrix A that defines the constraints will be a sparse matrix. An interior point approach will be used and, to obtain global convergence, large-scale trust-region problems will be solved. The objective function will be continuous, but the package will also work with LOVO (Low-Order Value Optimization) functions, with relaxed differentiability. The project points to the elaboration of a software that represents the "state-of-art" in this field. John L. C. Gardenghi was medalist in the III Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP 2007). Between 2008 and 2009 he participated in a junior undergraduate research, supported by CNPq. From 2009 to 2011, he was involved in a undergraduated research also supported by CNPq, under supervision of Prof. Sandra Augusta Santos, from IMECC-UNICAMP. In January and February of this year, the student attended, in the context of the summer school in IME-USP, the course MAT4302 - Tópicos de Álgebra Linear, when he got a A grade. The development of this project will count on the participation of collaborators from other institutions. In this context, Prof. Jose Mario Martinez and Prof. Sandra Augusta Santos, from IMECC-UNICAMP, will be special collaborators. It is planned an intense interaction with these specialists.

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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)
J.L.C. GARDENGHI; S.A. SANTOS. Métodos de regiões de confiança para resolução do problema de quadrados mínimos: implementação e testes numéricos. TEMA (São Carlos), v. 14, n. 1, p. 69-80, . (12/05725-0)
BIRGIN, E. G.; GARDENGHI, J. L.; MARTINEZ, J. M.; SANTOS, S. A.. On the solution of linearly constrained optimization problems by means of barrier algorithms. Top, v. 29, n. 2, . (12/05725-0, 13/07375-0, 18/24293-0)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
GARDENGHI, John Lenon Cardoso. A feasible primal-dual interior-point method for large-scale linearly constrained minimization. 2014. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.