Avviso di seminario - Prof. Giancarlo Bigi

Giorno 20 febbraio alle ore 12,00 presso l'aula Anile il prof. Giancarlo Bigi (Università di Pisa) terrà un seminario dal titolo: Algorithms for quasi-equilibria.
 

Abstract: The quasi-equilibrium problem (QEP) is a quite natural generalization of the so-called abstract equilibrium problem (EP) where the constraints are given through a set-valued map describing how the feasible region changes together with the considered point. QEPs are modeled upon quasi-variational inequalities (QVIs) and generalized Nash equilibrium problems (GNEPs). As EP subsumes optimization, multiobjective optimization, variational inequalities, fixed point and complementarity problems, Nash equilibria in noncooperative games and inverse optimization in a unique mathematical model, further “quasi” type models could be analysed through the QEP format beyond QVIs and GNEPs.

Unlikely QVI and GNEP, algorithms for the QEP format did not receive much attention. The goal of the talk is to discuss possible extensions of two  classical algorithmic approaches for optimization and VIs to QEPs, i.e., fixed point and extragradient methods. The main difficulties arise from the moving feasible region: the iterates belong to different sets and any solution of QEP has to be a fixed point of the constraining set-valued map. Therefore, a range of convexity, monotonicity and Lipschitz assumptions both on the equilibrium bifunction and the constraining set-valued map must be met in suitable combinations to achieve convergence.