Large-scale linearly constrained minimization with convergence to second order stationary points

• Grant number: 13/23494-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2014
• End date: April 30, 2017
• 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
• Associated research grant: 13/05475-7 - Computational methods in optimization, AP.TEM

Abstract

It is intended to consolidate a method (and its computational implementation) to minimize functions subject to equality and inequality linear constraints. The emphasis will be given to the convergence to second order stationary points. The number of variables and constraints will be large and, in general, the matrix A that defines the constraints will be sparse. We will use an interior point approach and, to obtain global convergence, we will solve large-scale trust-region subproblems. This project is a natural continuation of the candidate's masters work, supported by Fapesp (process 2012/05725-0), whose practical results have been excellent. It is worth to tell that the candidate was medalist in the III Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP 2007). 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 the Departament of Applied Mathematics from Unicamp, will be special collaborators. It is planned an intense interaction with these specialists. (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)

BIRGIN, E. G.; GARDENGHI, J. L.; MARTINEZ, J. M.; SANTOS, S. A.; TOINT, PH. L.. Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. MATHEMATICAL PROGRAMMING, v. 163, n. 1-2, p. 359-368, MAY 2017. (13/03447-6, 10/10133-0, 13/23494-9, 13/05475-7, 13/07375-0)

BIRGIN, E. G.; GARDENGHI, J. L.; MARTINEZ, J. M.; SANTOS, S. A.; TOINT, PH. L.. EVALUATION COMPLEXITY FOR NONLINEAR CONSTRAINED OPTIMIZATION USING UNSCALED KKT CONDITIONS AND HIGH-ORDER MODELS. SIAM JOURNAL ON OPTIMIZATION, v. 26, n. 2, p. 951-967, 2016. (13/07375-0, 13/23494-9, 13/05475-7, 10/10133-0, 13/03447-6)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GARDENGHI, John Lenon Cardoso. Complexity in nonlinear programmin. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.