On Generalized Variational Inequalities Involving Relaxed Lipschitz and Relaxed Monotone Operators

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Systems of relaxed cocoercive generalized variational inequalities via nonexpansive mappings ∗

In this paper, we consider a system of generalized variational inequalities. We introduce an iterative algorithm for the system of generalized variational inequalities and study the algorithmic convergence analysis. Strong convergence theorems are established. The results presented in this paper mainly improve and extend the corresponding results announced by many others. AMS subject classifica...

A New System of Generalized Nonlinear Relaxed Cocoercive Variational Inequalities

We introduce and study a new system of generalized nonlinear relaxed cocoercive inequality problems and construct an iterative algorithm for approximating the solutions of the system of generalized relaxed cocoercive variational inequalities in Hilbert spaces. We prove the existence of the solutions for the system of generalized relaxed cocoercive variational inequality problems and the converg...

Generalized Projection Method for Non-lipschitz Multivalued Monotone Variational Inequalities

We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...

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)...