Complementarity measures in optimality conditions

• Grant number: 19/13096-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: August 01, 2019
• End date: March 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Nicolas Esteban Fuentealba Armijo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/24293-0 - Computational methods in optimization, AP.TEM

Abstract

In the context of necessary optimality condition for nonlinear optimization and semidefinite optimization, the complementarity measure may be defined in several equivalent ways. However, in its sequential counterparts, where no constraint qualification is assumed, the way the complementarity is defined impacts the strength of the optimality condition. Our goul in this project is to study sequential optimality conditions in several contexts, which differ in the way complementarity is measured while measuring its impact in proving global convergence for several classes of algorithms. (AU)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

ARMIJO, NICOLAS F.; BELLO-CRUZ, YUNIER; HAESER, GABRIEL. On the convergence of iterative schemes for solving a piecewise linear system of equations. Linear Algebra and its Applications, v. 665, p. 24-pg., 2023-02-22. (19/13096-2, 18/24293-0)

ARMIJO, NICOLAS F.; GOMEZ, WALTER; CONCHA, JUAN P.. On the exactness of a simple relaxation for the extended Celis-Dennis-Tapia subproblem. OPTIMIZATION, v. N/A, p. 26-pg., 2022-07-01. (20/07421-5, 19/13096-2)

ARMIJO, NICOLAS F.; BELLO-CRUZ, YUNIER; HAESER, GABRIEL. A semi-smooth Newton method for general projection equations applied to the nearest correlation matrix problem. OPTIMIZATION, v. N/A, p. 23-pg., 2025-08-20. (19/13096-2, 23/08706-1)

Academic Publications

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

ARMIJO, Nicolas Esteban Fuentealba. A semi-smooth Newton method for conic projection equations.. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.