324. Projected solutions for quasi-equilibria
Invited abstract in session FC-2: Algorithms for Variational inequalities and equilibria, stream Advances in first-order optimization.
Friday, 11:25 - 12:40Room: M:O
Authors (first author is the speaker)
| 1. | Giancarlo Bigi
|
| Dipartimento di Informatica, Universita' di Pisa |
Abstract
The concept of a projected solution for quasi-variational inequalities and generalized Nash equilibrium problems was recently introduced, due to the modeling of deregulated electricity markets where the constraint map is not a self-map.
In this talk we show that the projected solutions of a quasi-equilibrium problem correspond to the classical solutions of an auxiliary quasi-equilibrium problem. This can be achieved by doubling the number of variables and adding an appropriate term. In this way algorithms for quasi-equilibria can be exploited for computing projected equilibria through the auxiliary problem. However, its structure does not guarantee the fulfilment of the assumptions required for the convergence of algorithms. In particular, descent and extragradient algorithms need that each feasible point is a fixed point for the constraint map and this not true in the case at hand. Thus, we show that under suitable assumption an ad-hoc choice of parameters allows convergence of the extragradient algorithm without the above requirement. the results of preliminary numerical tests are reported as well.
The talk is based on joint papers with Marco Castellani and Sara Latini.
Keywords
- Complementarity and variational problems
- Linear and nonlinear optimization
Status: accepted
Back to the list of papers