Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

Algorithms for Bilevel Pseudomonotone Variational Inequality Problems

We propose easily implementable algorithms for minimizing the norm with pseudomonotone variational inequality constraints. This bilevel problem arises in the Tikhonov regularization method for pseudomonone variational inequalities. Since the solution set of the lower variational inequality is not given explicitly, the available methods of mathematical programming and variational inequality can ...

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...

Double Projection Neural Network Model for Solving Pseudomonotone Variational Inequalities

In this paper we propose a novel double projection recurrent neural network model for solving pseudomonotone variational inequalities based on a technique of updating the state variable and fixed point theorem. This model is stable in the sense of Lyapunov and globally convergent for problems that satisfy Lipschitz continuity and pseudomonotonicity conditions. The global exponential stability o...

Research Article Nonlinear Vector Variational Inequality Problems for -Pseudomonotone Maps

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...