Second-order algorithms for nonlinear optimization with strong optimality properties

• Grant number: 17/12187-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2018
• End date: February 28, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Thiago Parente da Silveira
• 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): 20/00130-5 - Second-order optimality conditions for nonlinear programming, BE.EP.DR

Abstract

This project deals with the general nonlinear optimization problem in euclidean space with twice continuously differentiable function. Relating to second-order necessary optimality condition, there is a gap between conditions that can be proved (theoretical) and conditions that can be attained by an iterative algorithm (practical), in the sense that the theoretical ones are at the present time much stronger than the practical ones. The goal of this project is to reduce this gap, developing a practical second-order algorithm with better properties with respect to optimality. The relevance of this work is given by the practical need to develop algorithms that not only generate first-order stationary points, but also, that provide better guaranties of optimality. (AU)

Scientific publications

(4)

(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.; 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)

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; 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVEIRA, Thiago Parente da. Constant rank-type constraint qualifications and second-order optimality conditions. 2023. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.