Second-order optimality conditions and algorithms

• Grant number: 17/18308-2
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2018
• End date: 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
• City of the host institution: São Paulo

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)

Scientific publications

(37)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

BUENO, LUIS FELIPE; HAESER, GABRIEL; SANTOS, LUIZ-RAFAEL. Towards an efficient augmented Lagrangian method for convex quadratic programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, DEC 2019. (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, NOV 2019. (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, APR 2021. (18/24293-0, 17/12187-9, 17/18308-2, 13/07375-0)

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. (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, JUL 2021. (13/07375-0, 18/24293-0, 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., 2022-03-01. (18/24293-0, 17/18308-2, 13/07375-0)

OVIEDO, HARRY; ANDREANI, ROBERTO; RAYDAN, MARCOS. A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization. NUMERICAL ALGORITHMS, NOV 2021. (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, DEC 2021. (13/07375-0, 17/18308-2, 18/24293-0, 17/17840-2, 13/05475-7)

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. (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, JUL 2020. (13/05475-7, 18/24293-0, 17/18308-2)

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., 2022-04-21. (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., 2022-06-27. (17/12187-9, 18/24293-0, 13/07375-0, 17/17840-2, 20/00130-5, 17/18308-2)

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., 2021-04-07. (17/18308-2, 18/24293-0, 13/07375-0, 17/12187-9)

ANDREANI, ROBERTO; HAESER, GABRIEL; PRADO, RENAN WILLIAM; SCHUVERDT, MARIA L.; SECCHIN, LEONARDO D.. Global Convergence of a Second-order Augmented Lagrangian Method Under an Error Bound Condition. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 206, n. 2, p. 30-pg., 2025-08-01. (24/12967-8, 13/07375-0, 23/08621-6, 17/18308-2, 23/08706-1, 18/24293-0)

ANDREANI, R.; HAESER, G.; SCHUVERDT, M. L.; SECCHIN, L. D.. A RELAXED QUASINORMALITY CONDITION AND THE BOUNDEDNESS OF DUAL AUGMENTED LAGRANGIAN SEQUENCES. SIAM JOURNAL ON OPTIMIZATION, v. 35, n. 4, p. 16-pg., 2025-01-01. (18/24293-0, 13/07375-0, 24/12967-8, 17/18308-2)

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., 2019-11-08. (17/18308-2, 18/24293-0, 13/05475-7)

ANDREANI, ROBERTO; HAESER, GABRIEL; MITO, LEONARDO M.; RAMIREZ, HECTOR. A minimal face constant rank constraint qualification for reducible conic programming. MATHEMATICAL PROGRAMMING, v. N/A, p. 27-pg., 2025-05-24. (17/17840-2, 13/07375-0, 17/18308-2, 23/08706-1, 18/24293-0)

ANDREANI, ROBERTO; RAYDAN, MARCOS. Properties of the delayed weighted gradient method. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 78, n. 1, p. 167-180, JAN 2021. (17/18308-2, 13/05475-7)

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., 2022-05-25. (17/18308-2, 13/07375-0)

ANDREANI, ROBERTO; SCHUVERDT, MARIA L.; SECCHIN, LEONARDO D.. ON ENHANCED KKT OPTIMALITY CONDITIONS FOR SMOOTH NONLINEAR OPTIMIZATION. SIAM JOURNAL ON OPTIMIZATION, v. 34, n. 2, p. 25-pg., 2024-01-01. (13/07375-0, 17/18308-2, 18/24293-0)

ANDREANI, R.; HAESER, G.; RAMOS, A.; SANTOS, D. O.; SECCHIN, L. D.; SERRANONI, A.. Strong global convergence properties of algorithms for nonlinear symmetric cone programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. N/A, p. 25-pg., 2025-01-15. (17/18308-2, 18/24293-0, 23/01655-2, 13/07375-0)

BUENO, L. F.; HAESER, G.; LARA, F.; ROJAS, F. N.. An Augmented Lagrangian method for quasi-equilibrium problems. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, FEB 2020. (17/18308-2, 18/24293-0, 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, SI, p. 767-800, JUL 2020. (18/24293-0, 17/18308-2, 15/02528-8)

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)

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; VIANA, DAIANA S.. Optimality conditions and global convergence for nonlinear semidefinite programming. MATHEMATICAL PROGRAMMING, v. 180, n. 1-2, p. 203-235, MAR 2020. (17/18308-2, 13/05475-7)

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)

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)

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. (15/02528-8, 17/18308-2, 13/05475-7)

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., 2022-07-02. (13/07375-0, 17/18308-2, 13/05475-7)

ANDREANI, ROBERTO; COUTO, KELVIN R.; FERREIRA, ORIZON P.; HAESER, GABRIEL. CONSTRAINT QUALIFICATIONS AND STRONG GLOBAL CONVERGENCE PROPERTIES OF AN AUGMENTED LAGRANGIAN METHOD ON RIEMANNIAN MANIFOLDS. SIAM JOURNAL ON OPTIMIZATION, v. 34, n. 2, p. 27-pg., 2024-01-01. (17/17840-2, 23/08706-1, 17/18308-2, 18/24293-0, 13/07375-0)

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)

ANDREANI, ROBERTO; FUKUDA, ELLEN H.; HAESER, GABRIEL; SANTOS, DAIANA O.; SECCHIN, LEONARDO D.. Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 200, n. 1, p. 33-pg., 2023-12-07. (13/07375-0, 17/18308-2, 18/24293-0)

ANDREANI, ROBERTO; RAMOS, ALBERTO; SECCHIN, LEONARDO D.. IMPROVING THE GLOBAL CONVERGENCE OF INEXACT RESTORATION METHODS FOR CONSTRAINED OPTIMIZATION PROBLEMS\ast. SIAM JOURNAL ON OPTIMIZATION, v. 34, n. 4, p. 27-pg., 2024-01-01. (13/07375-0, 17/18308-2, 18/24293-0, 23/08706-1)

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., 2019-12-16. (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., 2020-02-21. (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., 2020-03-01. (18/24293-0, 13/05475-7, 17/18308-2, 17/17840-2, 16/16999-5)