| Full text | |
| Author(s): |
Andreani, R.
;
Haeser, G.
;
Ramos, A.
;
Santos, D. O.
;
Secchin, L. D.
;
Serranoni, A.
Total Authors: 6
|
| Document type: | Journal article |
| Source: | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. N/A, p. 25-pg., 2025-01-15. |
| Abstract | |
Sequential optimality conditions have played a major role in establishing strong global convergence properties of numerical algorithms for many classes of optimization problems. In particular, the way complementarity is handled defines different optimality conditions and is fundamental to achieving a strong condition. Typically, one uses the inner product structure to measure complementarity, which provides a general approach to conic optimization problems, even in the infinite-dimensional case. In this paper we exploit the Jordan algebraic structure of symmetric cones to measure complementarity, resulting in a stronger sequential optimality condition related to the well-known complementary approximate Karush-Kuhn-Tucker conditions in standard nonlinear programming. Our results improve some known results in the setting of semidefinite programming and second-order cone programming in a unified framework. In particular, we obtain global convergence that are stronger than those known for augmented Lagrangian and interior point methods for general symmetric cones. (AU) | |
| FAPESP's process: | 17/18308-2 - Second-order optimality conditions and algorithms |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 23/01655-2 - Optimality conditions and algorithms for conic optimization and applications in economics |
| Grantee: | Daiana Oliveira dos Santos |
| Support Opportunities: | Regular Research Grants |
| 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 |