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.

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, 2013-04-00. (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, MAY 2020. (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.