Iterative method for split equilibrium problem and minimization problem via conjugate gradient method

Abstract

In this work, we devise an accelerated iterative method for solving the common solution of split equilibrium problems and minimization problems. The idea is to construct an iterative scheme with fast convergence properties by blending the conjugate gradient direction with an averaging technique. Furthermore, the proposed method does not require prior knowledge of the operator norm of the bounded linear operator involved for implementation. Instead, the stepsizes are self adaptively updated. Under some standard conditions, we show that the sequence generated by the proposed algorithm converges weakly to the common solution of the considered problem. Numerical illustrations indicate that the proposed algorithm is easy to implement and computationally efficient.