Self-Adaptive Extragradient Algorithms for Quasi-Equilibrium Problems

We propose two iterative algorithms for solving two classes of quasi-equilibrium problems in Hilbert spaces: pseudomonotone and quasimonotone ones. The algorithms combine the subgradient method and the projection method with self-adaptive step sizes. Convergence of our proposed algorithms requires a condition that is milder than the one commonly used in the existing papers. Numerical experiments show that our algorithms are efficient and competitive to other extragradient-type, projection-type, and proximal point algorithms in solving the problem.