A New Projection Method for Variational Inequality Problems

A New Projection Method for Variational Inequality Problems∗

We propose a new projection algorithm for solving the variational inequality problem, where the underlying function is continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudomonotone). The method is simple and admits a nice geometric interpretation. It consists of two steps. First, we construct an appropriate hyperplane which strictly separates the current...

A New Projection-type Alternating Direction Method for Monotone Variational Inequality Problems

In this paper, we design a new projection-type alternating direction method which is an attractive method for solving variational inequality problems, and its application range covers linear programming, semidefinite programming etc. In each iteration, it just solves a linear equation and implements three orthogonal projections to closed convex sets. Under the conditions of monotonicity and Lip...

A New Version of Extragradient Method for Variational Inequality Problems

In this paper, we propose a new version of extragradient method for the variational inequality problem. The method uses a new searching direction which differs from any one in existing projection-type methods, and is of a better stepsize rule. Under a certain generalized monotonicity condition, it is proved to be globally convergent. @ 2001 Eisevier Science Ltd. All rights reserved. Keywords-Vs...

The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces

and Applied Analysis 3 4 if E is a reflexive, strictly convex, and smooth Banach space, then for all x, y ∈ E, φ ( x, y ) 0 iff x y. 1.7 For more details see 2, 3 . Let C be a closed convex subset of E, and let T be a mapping from C into itself. We denote by F T the set of fixed point of T . A point p in C is said to be an asymptotic fixed point of T 8 if C contains a sequence {xn}which converg...

A New Projection Algorithm for Generalized Variational Inequality