A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces

We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by proposed converges strongly to solution of problem under assumption set associated Minty nonempty. Compared with existing methods, we do not employ Fejér monotonicity strategy proving convergence. This comes from projecting fixed point instead current onto subset feasible at each iteration. Moreover, employing an Armijo-linesearch without subgradient has great advantage CPU-time. Some numerical experiments demonstrate efficiency strength presented algorithm.