A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces
Abstract
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 the proposed algorithm converges strongly to a solution of the equilibrium problem under the assumption that the solution set of the associated Minty equilibrium problem is nonempty. Compared with existing methods, we do not employ Fej\'{e}r monotonicity in the strategy of proving the convergence. This comes from projecting a fixed point instead of the current point onto a subset of the feasible set at each iteration. Moreover, employing an Armijo-linesearch without subgradient has a great advantage in CPU-time. Some numerical experiments demonstrate the efficiency and strength of the presented algorithm.
Cite
@article{arxiv.2006.04022,
title = {A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces},
author = {Lanmei Deng and Rong Hu and Yaping Fang},
journal= {arXiv preprint arXiv:2006.04022},
year = {2021}
}