In this paper, we introduce a modified extragradient approximation method for finding the common element of the set of fixed points of nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Ou...

Keywords--Variat ional inequalities, Projection method, Fixed point, Convergence. 1. I N T R O D U C T I O N Variational inequalities.have had a great impact and influence in the development of almost all branches of pure and applied sciences. There are a substantial number of numerical methods including projection, the WieneroHopf equations, auxiliary principle techniques for solving variation...

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing non-null normal vectors of the feasible set. In particular, two conceptual algorithms are proposed and each of them has three different variants which are related to modified extragradient algorithms. Our analysis contains two main parts: The first part contains two differ...

This paper proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the convergence of the iterative sequences and the range of application of the method is given. Mathematics Subject Classification (2010). 47J20, 49J40, 49M30.

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F (S) of a nonexpansive mapping S and the set of solutions ΩA of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approxi...

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion proper...

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal O(1/k) rate of convergence. Compared to the optimal non-SP algorithms, our...

Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like a...