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| Author(s): |
Thiago Parente da Silveira
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2023-12-04 |
| Examining board members: |
Gabriel Haeser;
Roberto Andreani;
Mituhiro Fukuda;
Flávia Morgana de Oliveira Jacinto;
Roberto Cristóvão Mesquita Silva
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| Advisor: | Gabriel Haeser; Hector Ariel Ramirez Cabrera |
| Abstract | |
The constant rank constraint qualification, introduced by Janin in [Math. Program. Study 21:110-126, 1984], has been shown very robust in diverse applications, such as global convergence of algorithms, second-order optimality conditions, computing the derivative of the value function, and stability analysis, but always in the nonlinear programming context. In this thesis, we propose different approaches to defining a constant rank-type constraint qualification for nonlinear second-order cone programming problems, that may be based either on the sequential optimality condition and then provide global convergence of an augmented Lagrangian algorithm, or a sequential approach based on the eigenvectors structure of the second-order cone and then get global convergence of algorithms based on an external penalty method, or a classical approach based on a constant rank theorem and then guarantees second-order necessary optimality condition based on the critical cone and holds for any Lagrange multiplier. (AU) | |
| FAPESP's process: | 17/12187-9 - Second-order algorithms for nonlinear optimization with strong optimality properties |
| Grantee: | Thiago Parente da Silveira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |