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Second-order optimality conditions and algorithms

Grant number: 17/18308-2
Support Opportunities:Regular Research Grants
Duration: February 01, 2018 - January 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Gabriel Haeser
Grantee:Gabriel Haeser
Host 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 (29)
(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, 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, . (13/07375-0, 17/18308-2, 13/05475-7)
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, . (13/05475-7, 18/24293-0, 17/18308-2)
BUENO, LUIS FELIPE; HAESER, GABRIEL; SANTOS, LUIZ-RAFAEL. Towards an efficient augmented Lagrangian method for convex quadratic programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, . (17/18308-2, 15/02528-8, 18/24293-0)
HAESER, G.; RAMOS, A.. New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, . (13/05475-7, 18/24293-0, 17/18308-2)
ANDREANI, R.; FUKUDA, E. H.; HAESER, G.; RAMIREZ, H.; SANTOS, D. O.; SILVA, P. J. S.; SILVEIRA, T. P.. rratum to: New Constraint Qualifications and Optimality Conditions for Second Order Cone Program. Set-Valued and Variational Analysis, v. 30, n. 1, . (18/24293-0, 17/12187-9, 17/18308-2, 13/07375-0)
ANDREANI, ROBERTO; CARVALHO, RUI M.; SECCHIN, LEONARDO D.; SILVA, GILSON N.. Convergence of quasi-Newton methods for solving constrained generalized equations*. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, v. 28, p. 24-pg., . (17/18308-2, 13/07375-0)
ANDREANI, R.; CUSTODIO, A. L.; RAYDAN, M.. Using first-order information in direct multisearch for multiobjective optimization. OPTIMIZATION METHODS & SOFTWARE, v. N/A, p. 22-pg., . (17/18308-2, 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, 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, . (13/07375-0, 18/24293-0, 17/18308-2)
OVIEDO, HARRY; ANDREANI, ROBERTO; RAYDAN, MARCOS. A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization. NUMERICAL ALGORITHMS, . (13/05475-7, 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, . (13/07375-0, 17/18308-2, 18/24293-0, 17/17840-2, 13/05475-7)
ANDREANI, ROBERTO; RAYDAN, MARCOS. Properties of the delayed weighted gradient method. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 78, n. 1, p. 167-180, . (17/18308-2, 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., . (17/12187-9, 18/24293-0, 13/07375-0, 17/17840-2, 20/00130-5, 17/18308-2)
ANDREANI, R.; HAESER, G.; SCHUVERDT, M. L.; SECCHIN, L. D.; SILVA, P. J. S.. On scaled stopping criteria for a safeguarded augmented Lagrangianmethod with theoretical guarantees. MATHEMATICAL PROGRAMMING COMPUTATION, v. 14, n. 1, p. 26-pg., . (18/24293-0, 17/18308-2, 13/07375-0)
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, v. 30, n. 1, p. 5-pg., . (17/18308-2, 18/24293-0, 13/07375-0, 17/12187-9)
HAESER, G.; RAMOS, A.. New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 184, n. 2, p. 13-pg., . (17/18308-2, 18/24293-0, 13/05475-7)
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., . (17/18308-2, 18/24293-0, 13/07375-0, 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., . (17/12187-9, 18/24293-0, 20/00130-5, 13/07375-0, 17/18308-2, 17/17840-2)
ANDREANI, R.; OVIEDO, H.; RAYDAN, M.; SECCHIN, L. D.. An extended delayed weighted gradient algorithm for solving strongly convex optimization problems. Journal of Computational and Applied Mathematics, v. 416, p. 19-pg., . (13/07375-0, 17/18308-2, 13/05475-7)
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, p. 34-pg., . (17/18308-2, 18/24293-0, 15/02528-8)
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, p. 30-pg., . (17/18308-2, 18/24293-0, 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, p. 21-pg., . (18/24293-0, 13/05475-7, 17/18308-2, 17/17840-2, 16/16999-5)
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)
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, . (17/18308-2, 13/05475-7)
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., . (17/18308-2, 18/24293-0, 17/17840-2)
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, . (18/24293-0, 17/18308-2, 15/02528-8)
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, . (15/02528-8, 17/18308-2, 13/05475-7)
BUENO, L. F.; HAESER, G.; LARA, F.; ROJAS, F. N.. An Augmented Lagrangian method for quasi-equilibrium problems. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, . (17/18308-2, 18/24293-0, 13/05475-7)
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., . (17/18308-2, 18/24293-0, 17/17840-2)

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