Abstract
We study the existence of projected solutions for generalized Nash equilibrium problems defined in Banach spaces, under mild convexity assumptions for each loss function and without lower semicontinuity assumptions on the constraint maps. Our approach is based on Himmelberg’s fixed point theorem. As a consequence, we also obtain existence of projected solutions for quasi-equilibrium problems and quasi-variational inequalities. Finally, we show the existence of projected solutions for Single-Leader–Multi-Follower games.
| Original language | English |
|---|---|
| Pages (from-to) | 344-362 |
| Number of pages | 19 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 191 |
| Issue number | 1 |
| Early online date | 27 Sep 2021 |
| DOIs | |
| State | Published - Oct 2021 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Fixed point
- Generalized convexity
- Generalized Nash equilibrium
- Non-self-map
- Quasi-equilibrium problems
- Quasi-variational inequalities