On monotone variational inequalities with random data

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...

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...

Recession Methods in Monotone Variational Hemivariational Inequalities

Throughout the paper we use standard notations except special symbols introduced when they are defined. All spaces considered are Banach spaces whose norms are always denoted by ‖ · ‖. For any space V we consider its dual space V ? equipped with the strong topology. We denote by 〈·, ·〉 the duality pairing between V and V . Let f : V → R ∪ {∞} be an extended-real-valued function. Identifying ext...

An Explicit Algorithm for Monotone Variational Inequalities

We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto C are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under the only assumptions of continuity and monotonicity of the operator and existence of solutions.