STRONG STRONG CONVERGENCE ALGORITHMS FOR EQUILIBRIUM PROBLEMS WITHOUT MONOTONICITY

B. V.  Dinh; N. T.  Thanh ha; N. N.  Hai; T. T. H.  Thanh

STRONG STRONG CONVERGENCE ALGORITHMS FOR EQUILIBRIUM PROBLEMS WITHOUT MONOTONICITY

Authors

B. V. Dinh Department of Mathematics, Faculty of Information Technology,Le Quy Don Technical University, Hanoi, Vietnam
N. T. Thanh ha Department of Mathematics, Faculty of Information Technology,Le Quy Don Technical University, Hanoi, Vietnam
N. N. Hai Department of Scientific Fundamentals, Vietnam Trade Union University, Hanoi, Vietnam
T. T. H. Thanh Department of Mathematics, Faculty of Information Technology,Le Quy Don Technical University, Hanoi, Vietnam

Keywords:

Non-monotonicity, equilibria, shrinking projection methods, strong convergence, Armijo linesearch, Hilbert space

Abstract

In this paper, we introduce two new line search algorithms for solving a non-monotone equilibrium problem in a real Hilbert space. Each method can be considered as a combination of the extragradient method with line search and shrinking projection methods. Then we show that the iterative sequence generated by each method converges strongly to a solution of the considered problem. A numerical example is also provided.