| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil
[2] Univ Sao Paulo, Inst Math & Stat, Dept Appl Math, Sao Paulo, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON OPTIMIZATION; v. 29, n. 1, p. 31-54, 2019. |
| Web of Science Citations: | 3 |
| Abstract | |
Generalized Nash equilibrium problems (GNEPs) are a generalization of the classic Nash equilibrium problems (NEPs), where each player's strategy set depends on the choices of the other players. In this work we study constraint qualifications (CQs) and optimality conditions tailored for GNEPs, and we discuss their relations and implications for global convergence of algorithms. We show the surprising fact that, in contrast to the case of nonlinear programming, in general the Karush-Kuhn-Tucker (KKT) residual cannot be made arbitrarily small near a solution of a GNEP. We then discuss some important practical consequences of this fact. We also prove that this phenomenon is not present in an important class of GNEPs, including NEPs. Finally, under an introduced weak CQ, we prove global convergence to a KKT point of an augmented Lagrangian algorithm for GNEPs, and under the quasi-normality (QN) CQ for GNEPs, we prove boundedness of the dual sequence. (AU) | |
| FAPESP's process: | 15/02528-8 - Newton-type methods for linear and nonlinear optimization |
| Grantee: | Luis Felipe Cesar da Rocha Bueno |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 17/18308-2 - Second-order optimality conditions and algorithms |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/05475-7 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |