| Texto completo | |
| Autor(es): |
Andreani, Roberto
;
Haeser, Gabriel
;
Mito, Leonardo M.
;
Ramirez, Hector
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | MATHEMATICAL PROGRAMMING; v. N/A, p. 27-pg., 2025-05-24. |
| Resumo | |
In a previous paper [Andreani et al, Math. Prog. 202, p. 473-514, 2023] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all faces of the underlying cone. This condition is independent of Robinson's condition and it implies a strong second-order necessary optimality condition which depends on a single Lagrange multiplier instead of the full set of Lagrange multipliers. In this paper we expand on this result in several directions, namely, we consider the larger class of C2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}<^>2-$$\end{document}cone reducible constraints and we show that it is not necessary to consider all faces of the cone; instead a single specific face should be considered (which turns out to be weaker than Robinson's condition) in order for the first order necessary optimality condition to hold. This gives rise to a notion of facial reduction for nonlinear conic programming, that allows locally redefining the original problem only in terms of this specific face instead of the whole cone, providing a more robust formulation of the problem in which Robinson's condition holds. We were also able to prove the strong second-order necessary optimality condition in this context by considering only the subfaces of this particular face, which is a new result even in nonlinear programming. (AU) | |
| Processo FAPESP: | 17/17840-2 - Estimativas de erro em otimização não linear |
| Beneficiário: | Leonardo Makoto Mito |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |
| Processo FAPESP: | 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria |
| Beneficiário: | Francisco Louzada Neto |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |
| Processo FAPESP: | 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem |
| Beneficiário: | Gabriel Haeser |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 23/08706-1 - Métodos computacionais de otimização |
| Beneficiário: | Ernesto Julián Goldberg Birgin |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 18/24293-0 - Métodos computacionais de otimização |
| Beneficiário: | Sandra Augusta Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |