Convergence of inertial iterative algorithms based on auxiliary principle for linearly constrained monotone equilibrium problems

In this paper, inertial iterative algorithms based on auxiliary principle are proposed for solving linearly constrained monotone equilibrium problems (LCMEP) via an auxiliary principle, which is to construct an auxiliary equilibrium problem and show that a solution of the auxiliary problem is also a solution to the original problem.The convergence results of the inertial iterative algorithm are established under some mild assumptions.We obtain the worst-case convergence rate O(1/t) of the proposed algorithm in the nonergodic case.Furthermore, we propose an self-adaptive inertial iterative algorithm for solving LCMEP, which can improve the convergence rate and robustness of the non-adaptive inertial iterative algorithm and reduce the uncertainty caused by the selection of fixed inertia parameters.Some customized inertial iterative algorithms are also given by choosing special positive-definite matrix in auxiliary equilibrium problem.