| Full text | |
| Author(s): |
Andreani, Roberto
;
Haeser, Gabriel
;
Mito, Leonardo M.
;
Ramirez, Hector
Total Authors: 4
|
| Document type: | Journal article |
| Source: | MATHEMATICAL PROGRAMMING; v. N/A, p. 27-pg., 2025-05-24. |
| Abstract | |
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) | |
| FAPESP's process: | 17/17840-2 - Error estimation in nonlinear optimization |
| Grantee: | Leonardo Makoto Mito |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/18308-2 - Second-order optimality conditions and algorithms |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 23/08706-1 - Numerical optimization |
| Grantee: | Ernesto Julián Goldberg Birgin |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |