Development of efficient methods for conic linear and nonlinear optimization probl...
Numerical methods for Nash equilibrium problems with descent criteria
Siegfried andreas Fischer | technische universitat Dresden - Alemanha
| Full text | |
| Author(s): |
Prado, Renan W.
;
Santos, Sandra A.
;
Simoes, Lucas E. A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 197, n. 2, p. 32-pg., 2023-03-13. |
| Abstract | |
Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary approximate Karush-Kuhn-Tucker (WCAKKT) conditions. They are shown to be verified by limit points generated not only by safeguarded augmented Lagrangian methods, but also by inexact restoration methods, inverse and logarithmic barrier methods, and a penalized algorithm for constrained nonsmooth optimization. Under the analyticity of the feasible set description, and resting upon a desingularization result, the new conditions are proved to be equivalent to the CAKKT conditions. The WCAKKT conditions capture the algebraic elements of the desingularization result needed to characterize CAKKT sequences using a weighted complementarity condition that asymptotically sums zero. Due to its generality and strength, the new condition may help to enlighten the practical performance of algorithms in generating CAKKT sequences. (AU) | |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic 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 |
| FAPESP's process: | 16/22989-2 - A sampling method for constrained nonsmooth optimization problems |
| Grantee: | Lucas Eduardo Azevedo Simões |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 19/18859-4 - A continuous optimization method with stopping criterion based on a new sequential optimality condition |
| Grantee: | Renan Willian Prado |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |