Variational inequalities of perturbed maximal monotone mapping with applications

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 ...

On Monotone Variational Inequalities with Random Data

We study monotone variational inequalities with random data and give measurability, existence and uniqueness results in the general framework of a Hilbert space setting. Then we turn to the more structured case where a finite Karhunen-Loève expansion leads to a separation of the random and the deterministic variables. Here we present a discretization procedure with respect to the random variabl...

Variational Principles for Monotone and Maximal Bifunctions

We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.

Monotone Iterations for Eliptic Variational Inequalities

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...