Simple and Optimal Methods for Stochastic Variational Inequalities, I: Operator Extrapolation

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Operator-splitting Methods for General Mixed Variational Inequalities

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control

This paper applies splitting techniques developed for set-valued maximal monotone operators to monotone aane variational inequalities, including as a special case the classical linear comple-mentarity problem. We give a uniied presentation of several splitting algorithms for monotone operators, and then apply these results to obtain two classes of algorithms for aane variational inequalities. T...

Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with uncertain coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC finite element approach based on deterministic adaptive mesh refinement for the arising ”pathwise” problems and outline a convergence theory in terms of ...

Variational inequalities with operator solutions

The aim of the present paper is to give a new kind of point of view in the theory of variational inequalities. Our approach makes possible the study of both scalar and vector variational inequalities under a great variety of assumptions. One can include here the variational inequalities defined on reflexive or nonreflexive Banach spaces, as well as the vector variational inequalities defined on...