Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator

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 ...

Minimum Principle Sufficiency for a Variational Inequality with Pseudomonotone Mapping

For a variational inequality problem (VIP) with a psudomonotone mapping F on its solution set C∗, we give equivalent statements for C∗ to be determined by the zeroes Γ(c∗) of the primal gap function of VIP, where c∗ ∈ C∗. One sufficient condition is also presented in terms of weaker sharpness of C∗. With the psudomonotonicity∗ of F onC∗ being characterized, C∗ turns out to coincide with the zer...

Convergence and Stability of a Three-step Iterative Algorithm for a General Quasi-variational Inequality Problem

We consider a general quasi-variational inequality problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasivariational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variationa...

Research Article Nonlinear Vector Variational Inequality Problems for -Pseudomonotone Maps

A Two-stage Descent Method with Optimal Step-sizes for Monotone Variational Inequality Problems

In this paper, we propose a two-stage descent method for monotone variational inequality problems, which only needs functional values for given variables in the solution process. Under certain conditions, the global convergence of the method is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed method. AMS(2000) Subject Classification: 90C25, 90C30