Browder-Hartman-Stampacchia variational inequalities for multi-valued monotone operators

Proximal Methods for Variational Inequalities with Set-Valued Monotone Operators

A general approach to analyse convergence and rate of convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using regularization on a subspace and weak regularization. Th...

Variational Inequalities and Surjectivity for Set-valued Monotone Mappings

We denote by σ(F,E) the topology on F generated by the family {ω(x, ε) : x ∈ E, ε > 0} as a subbase for the neighbourhood system at 0. It is easy to show that, if F possesses the σ(F,E)-topology, F becomes a locally convex topological vector space. The σ(E,F )-topology on E is defined analogously. A subset X of E is said to be σ(E,F )-compact if X is compact related to the σ(E,F )-topology. Let...

Enlargement of Monotone Operators with Applications to Variational Inequalities

Given a point-to-set operator T, we introduce the operator T " deened as T " (x) = fu : hu ? v; x ? yi 0 for all y 2 R n ; v 2 T(y)g. When T is maximal monotone T " inherits most properties of the "-subdiierential, e.g. it is bounded on bounded sets, T " (x) contains the image through T of a suuciently small ball around x, etc. We prove these and other relevant properties of T " , and apply it ...

Regularization of Non-Monotone Multi-valued Variational Inequalities with Applications to Partitionable Problems

We consider a general coercivity condition for multi-valued variational inequalities and show that this condition ensures both convergence of the Tikhonov-Browder regularization method and existence of solutions to the initial and perturbed problems. Applications of this approach to partitionable multi-valued variational inequalities utilizing extensions of order monotonicity properties are als...

Monotone Iterations for Eliptic Variational Inequalities