A Class Of Optimization Methods For Generalized Nash Equilibrium Problem

Generalized Nash equilibrium problem is a generalization of the classical one. It is a core concept of non-cooperative game theory, where each player’s benefit function(also known as the compensation function) and feasible strategy sets depend on the strategies of other participants. Generalized Nash equilibrium problem has been widely used in the fields of economics, transportation, electricity markets, environmental governance, which promote the development and innovation of GNEP algorithm. At present,porpular schemes are as follow: firstly, reformulating it into a quasi-variational inequality problem(QVI); Second, reformulating it into an optimization problem with Nikaido-Isoda(regularization) function, gap function. In this paper,we mainly study generalized Nash equilibrium problem with sharing constraints, which is equivalent to smooth unconstrained optimization problems by NI regularization function, make some modifications about descent direction in the literature, and analyze its convergence.