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Error estimation in nonlinear optimization

Grant number: 17/17840-2
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): April 01, 2018
Effective date (End): March 16, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Gabriel Haeser
Grantee:Leonardo Makoto Mito
Home 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
Associated scholarship(s):19/24360-2 - Second-order optimality conditions for nonlinear conic programming, BE.EP.DR


In this project we will approach algorithms to the general smooth nonlinear optimization problem. Given that an algorithm has stopped due to satisfying its optimality criterium with some precision, we intend to estimate the distance between the output solution and an actual stationary point of the problem, imposing some weak hypothesis over it. This leads to an accurate quality measure of algorithmicaly generated solutions, instead of an implicit measure related to the approximate satisfaction of an optimality condition.

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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)
ANDREANI, ROBERTO; GOMEZ, WALTER; HAESER, GABRIEL; MITO, LEONARDO M.; RAMOS, ALBERTO. On Optimality Conditions for Nonlinear Conic Programming. MATHEMATICS OF OPERATIONS RESEARCH, p. 1-26, DEC 2021. Web of Science Citations: 1.
ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; RAMOS, ALBERTO; SECCHIN, LEONARDO D. On the best achievable quality of limit points of augmented Lagrangian schemes. NUMERICAL ALGORITHMS, OCT 2021. Web of Science Citations: 0.
BIRGIN, ERNESTO G.; GOMEZ, WALTER; HAESER, GABRIEL; MITO, LEONARDO M.; SANTOS, DAIANA O. An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem. COMPUTATIONAL & APPLIED MATHEMATICS, v. 39, n. 1 MAR 2020. Web of Science Citations: 0.

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