Galerkin Methods for Complementarity Problems and Variational Inequalities

Multigrid Methods for Obstacle Problems

Obstacle problems can be posed as elliptic variational inequalities, complementarity inequalities and Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this paper, we propose a multigrid algorithm based on the full approximate scheme (FAS) for solving the membrane constrained obstacle problems and the minimal surface obstacle problems in the formulations of HJB equations. ...

Forward-backward Resolvent Splitting Methods for General Mixed Variational Inequalities

We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known threestep forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for so...

Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities

We study discontinuous Galerkin methods for solving elliptic variational inequalities, of both the first and second kinds. Analysis of numerous discontinuous Galerkin schemes for elliptic boundary value problems is extended to the variational inequalities. We establish a priori error estimates for the discontinuous Galerkin methods, which reach optimal order for linear elements. Results from so...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Projection-proximal methods for general variational inequalities

In this paper, we consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known res...