Interior proximal methods for equilibrium programming: part II

In this article we discuss a method for solving equilibrium problems, introduced by Flam and Antipin [S.D. Flam and A.S. Antipin, Equilibrium programming using proximal-like algorithms, Math. Program.77 (1997), pp. 29-41]. We extend this method to unbounded feasible sets which e.g. also leads to the necessity of a new and appropriate stopping criteria. We also provide results permitting to use zone-coercive regularizing functionals (of Bregman type). For example, when the boundary of the feasible set has a certain curvature, the regularized subproblems can be treated as unconstrained ones.