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Error estimation in nonlinear optimization

Grant number: 17/17840-2
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): April 01, 2018
Effective date (End): February 28, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Gabriel Haeser
Grantee:Leonardo Makoto Mito
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
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, . (13/07375-0, 17/18308-2, 18/24293-0, 17/17840-2, 13/05475-7)
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, . (16/16999-5, 13/05475-7, 17/17840-2, 18/24293-0, 17/18308-2)
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, . (13/07375-0, 18/24293-0, 17/17840-2, 17/18308-2)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
MITO, Leonardo Makoto. Topics in nonlinear conic optimization and applications. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.

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