On variable-step relaxed projection algorithm for variational inequalities

A relaxed projection method for variational inequalities

where S is a nonempty closed convex subset o f R ' , f is a mapp ing f rom R" into itself, and ( . , .) denotes the inner p roduc t in R n. This problem is commonly called the variational inequality problem and has proved to be very useful in dealing with a variety o f equilibrium models. As in the cases o f nonl inear equat ions and nonl inear opt imizat ion problems, solutions o f problem (1)...

Finite-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities

A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous convex function inequality. In our scheme, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore,...

General Projection Systems and Relaxed Cocoercive Nonlinear Variational Inequalities

We explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces. 2000 Mathematics subject classification: primary 49J40, 65B05; secondary 47H20.

Two-step Systems for G-h-relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets o...