Interior point methods for equilibrium problems

In the present paper we discuss three methods for solving equilibrium-type fixed point problems. Concentrating on problems whose solutions possess some stability property, we establish convergence of these three proximal-like algorithms that promise a very high numerical tractability and efficiency. For example, due to the implemented application of zone coercive Bregman functions, all these methods allow to treat the generated subproblems as unconstrained and, partly, explicitly solvable ones.