Bilevel Programs and Nash games
From 14:00 to 14:25:
TITLE: Equilibria for semi-infinite programming
SPEAKER: Giancarlo Bigi (Dipartimento di Informatica, Università di Pisa)
ABSTRACT: Bilevel optimization, noncooperative games and semi-infinite programming share some similarities, which may lead to meaningful connections. Indeed, theoretical developments and algorithms developed for one of these models could be exploited to cope with the others. In this talk we focus on the relationships between generalized Nash games and semi-infinite programming. In particular, we show how generalized Nash games can be exploited to solve semi-infinite programs with convex-concave constraints, relying on penalization techniques and a sequence of suitable saddlepoint problems.
From 14:30 to 14:55:
TITLE: A bridge between bilevel programs and Nash games
SPEAKER: Lorenzo Lampariello (Dipartimento di Studi Aziendali, Università degli Studi Roma Tre)
ABSTRACT: We study connections between bilevel programming problems and Generalized Nash Equilibrium Problems (GNEP). We provide a complete analysis of the relationship between the vertical bilevel problem and the corresponding horizontal one-level GNEP. We define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of the GNEP. Our study provides the theoretical backbone and the main ideas uderlying some useful novel algorithmic developments.
From 15:00 to 15:25:
TITLE: A single-level approach to multi-leader-follower games
SPEAKER: Simone Sagratella (Dipartimento di Ingegneria Informatica Automatica Gestionale, Sapienza Università di Roma)
ABSTRACT: Multi-Leader Common-Follower games (MLCF) are a powerful modelling tool to study complex bilevel systems arising for example in electricity markets. Leveraging the optimal value approach, we introduce a Generalized Nash Equilibrium Problem (GNEP) model based on the first order approximation of follower’s value function. This single-level GNEP is closely related to the original MLCF. We show that any KKT point of (a suitably perturbed version of the) former problem is critical for (an approximate) MLCF. Moreover, we define wide classes of problems for which the vice-versa holds as well.