Mirror Frameworks for Relatively Lipschitz and Monotone-Like Variational Inequalities

Relatively monotone variational inequalities over product sets

New concepts of monotonicity which extend the usual ones are introduced for variational inequality problems over product sets. They enable us to strengthen existence results and extend the eld of applications of the solution methods. c © 2001 Elsevier Science B.V. All rights reserved.

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...

Interior projection-like methods for monotone variational inequalities

We propose new interior projection type methods for solving monotone variational inequalities. The methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms, and are based on using non Euclidean projection-like maps. We prove global convergence results and establish rate of convergence estimates. The projection-like maps are given by analytical formu...

Generalized Variational-like Inequalities with Compositely Monotone Multifunctions

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η − α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the so...

Monotone Iterations for Eliptic Variational Inequalities