Explicit iterative algorithms for solving equilibrium problems

Abstract

The paper introduces two new extragradient algorithms for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition recently presented by Mastroeni in auxiliary problem principle. The algorithm uses variable stepsizes which are updated at each iteration and based on some previous iterates. The advantage of the algorithms is that they are done without the prior knowledge of Lipschitz-type constants and also without any linesearch procedure. The convergence of the algorithms is established under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithms is formulated. Several of fundamental experiments are provided to illustrate the numerical behavior of the algorithms and also to compare with others.