A cutting hyperplane method for solving pseudomonotone non-Lipschitzian equilibrium problems

Abstract

Abstract We present a new method for solving equilibrium problems, where the underlying function is continuous and satisfies a pseudomonotone assumption. First, we construct an appropriate hyperplane which separates the current iterative point from the solution set. Then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the half-space containing the solution set. We also analyze the global convergence of the method under minimal assumptions. MSC: 65K10, 90C25.</jats:p