Error estimation in nonlinear optimization

• Grant number: 17/17840-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2018
• End date: 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

Abstract

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.

Scientific publications

(9)

(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; 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. (13/07375-0, 18/24293-0, 17/17840-2, 17/18308-2)

ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; RAMIREZ, HECTOR. Sequential Constant Rank Constraint Qualifications for Nonlinear Semidefinite Programming with Algorithmic Applications. Set-Valued and Variational Analysis, v. 31, n. 1, p. 27-pg., 2023-03-01. (17/18308-2, 18/24293-0, 17/17840-2)

ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; RAMIREZ, HECTOR; SILVEIRA, THIAGO P.. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. MATHEMATICAL PROGRAMMING, v. N/A, p. 41-pg., 2023-03-23. (17/12187-9, 18/24293-0, 20/00130-5, 13/07375-0, 17/18308-2, 17/17840-2)

FUKUDA, ELLEN H.; HAESER, GABRIEL; MITO, LEONARDO M.. On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming. Set-Valued and Variational Analysis, v. 31, n. 2, p. 28-pg., 2023-06-01. (17/18308-2, 18/24293-0, 17/17840-2)

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, p. 21-pg., 2020-03-01. (18/24293-0, 13/05475-7, 17/18308-2, 17/17840-2, 16/16999-5)

ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; RAMIREZ, HECTOR. Weak notions of nondegeneracy in nonlinear semidefinite programming. MATHEMATICAL PROGRAMMING, v. N/A, p. 32-pg., 2023-05-27. (17/18308-2, 18/24293-0, 13/07375-0, 17/17840-2)

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. (16/16999-5, 13/05475-7, 17/17840-2, 18/24293-0, 17/18308-2)

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. (13/07375-0, 17/18308-2, 18/24293-0, 17/17840-2, 13/05475-7)

ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; HECTOR RAMIREZ, C.; SILVEIRA, THIAGO P.. Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 195, n. 1, p. 37-pg., 2022-06-27. (17/12187-9, 18/24293-0, 13/07375-0, 17/17840-2, 20/00130-5, 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.