Newton-type methods for linear and nonlinear optimization

• Grant number: 15/02528-8
• Support type: Regular Research Grants
• Duration: June 01, 2015 - May 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Luis Felipe Cesar da Rocha Bueno
• Grantee: Luis Felipe Cesar da Rocha Bueno
• Home Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil

Abstract

In this research project we will present some alternatives for computational optimization methods. Our focus is to investigate Newton type methods and its relations with some optimization methods. Much of the research will be associated with the Inexact Restoration and type Augmented Lagrangian methods. In Inexact Restoration methods we plan to develop an algorithm that uses Newtonian techniques in its subproblems to take advantage of the good performance of Sequential Quadratic Programming methods, when it is possible. In addition, we hope to expand the convergence results for algorithms without derivatives. For Augmented Lagrangian methods we propose a very unusual idea of penalizing simple constraints. With this concept we hope to get significant results even in linear programming. Finally, we also intend to propose an efficient method for nonlinear programming that combines the advances made on the Inexact Restoration with the penalization of simple constraints to address inequalities. (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)

BUENO, LUIS FELIPE; HAESER, GABRIEL; ROJAS, FRANK NAVARRO. OPTIMALITY CONDITIONS AND CONSTRAINT QUALIFICATIONS FOR GENERALIZED NASH EQUILIBRIUM PROBLEMS AND THEIR PRACTICAL IMPLICATIONS. SIAM JOURNAL ON OPTIMIZATION, v. 29, n. 1, p. 31-54, 2019. Web of Science Citations: 2.

BIRGIN, E. G.; BUENO, L. F.; MARTINEZ, J. M. Sequential equality-constrained optimization for nonlinear programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 65, n. 3, p. 699-721, DEC 2016. Web of Science Citations: 4.

BUENO, L. F.; HAESER, G.; MARTINEZ, J. M. An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization. Optimization Letters, v. 10, n. 6, p. 1315-1325, AUG 2016. Web of Science Citations: 3.