ITERATIVE ALGORITHMS FOR EQUILIBRIUM PROBLEMS BASED ON PROXIMAL-LIKE METHODS

In this paper, we present two algorithms, namely Algorithm 1.2 and Algorithm 1.3, with most violated constraint control strategy used in the projection method for solving equilibrium problems. Compared with the projection methods, both algorithms are designed to avoid computing the projection to the nonlinear level set. Under certain conditions, the convergences of the Algorithm 1.2 and Algorithm 1.3 are established, and the linear convergence rate of Algorithm 1.3 is obtained. At last, some examples to illustrate the convergence performance of Algorithm 1.2 and Algorithm 1.3 are given.