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Second-order optimality conditions and algorithms

Grant number: 17/18308-2
Support type:Regular Research Grants
Duration: February 01, 2018 - January 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Gabriel Haeser
Grantee:Gabriel Haeser
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we present several lines of research on the use of second-order information in nonlinear programming problems. Being second-order optimality conditions more accurate with respect to optimality than its first-order counterparts, the advantages of a second-order algorithm is evident, given those recent applications of nonlinear programming where guaranteeing optimality is paramount. Research topics described involve this topic both from theoretical and practical perspectives. (AU)

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Scientific publications (15)
(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.
OVIEDO, HARRY; ANDREANI, ROBERTO; RAYDAN, MARCOS. A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization. NUMERICAL ALGORITHMS, NOV 2021. Web of Science Citations: 0.
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.
ANDREANI, R.; FUKUDA, E. H.; HAESER, G.; SANTOS, D. O.; SECCHIN, L. D. On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 79, n. 3, p. 633-648, JUL 2021. Web of Science Citations: 0.
ANDREANI, R.; FUKUDA, E. H.; HAESER, G.; RAMIREZ, H.; SANTOS, D. O.; SILVA, P. J. S.; SILVEIRA, T. P. Erratum to: New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs. Set-Valued and Variational Analysis, APR 2021. Web of Science Citations: 0.
ANDREANI, ROBERTO; RAYDAN, MARCOS. Properties of the delayed weighted gradient method. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 78, n. 1, p. 167-180, JAN 2021. Web of Science Citations: 0.
BUENO, L. F.; HAESER, G.; LARA, F.; ROJAS, F. N. An Augmented Lagrangian method for quasi-equilibrium problems. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 76, n. 3, SI, p. 737-766, JUL 2020. Web of Science Citations: 2.
BUENO, LUIS FELIPE; HAESER, GABRIEL; SANTOS, LUIZ-RAFAEL. Towards an efficient augmented Lagrangian method for convex quadratic programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 76, n. 3, SI, p. 767-800, JUL 2020. Web of Science Citations: 3.
ANDREANI, ROBERTO; HAESER, GABRIEL; VIANA, DAIANA S. Optimality conditions and global convergence for nonlinear semidefinite programming. MATHEMATICAL PROGRAMMING, v. 180, n. 1-2, p. 203-235, MAR 2020. Web of Science Citations: 1.
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.
BUENO, L. F.; HAESER, G.; LARA, F.; ROJAS, F. N. An Augmented Lagrangian method for quasi-equilibrium problems. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, FEB 2020. Web of Science Citations: 2.
BUENO, LUIS FELIPE; HAESER, GABRIEL; SANTOS, LUIZ-RAFAEL. Towards an efficient augmented Lagrangian method for convex quadratic programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, DEC 2019. Web of Science Citations: 0.
HAESER, G.; RAMOS, A. New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, NOV 2019. Web of Science Citations: 0.
ANDREANI, R.; HAESER, G.; SECCHIN, L. D.; SILVA, P. J. S. NEW SEQUENTIAL OPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS AND ALGORITHMIC CONSEQUENCES. SIAM JOURNAL ON OPTIMIZATION, v. 29, n. 4, p. 3201-3230, 2019. Web of Science Citations: 2.
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: 3.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.