Incremental constraint projection methods for variational inequalities

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Variational inequalities on Hilbert $C^*$-modules

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

Stochastic methods for large-scale linear problems, variational inequalities, and convex optimization

This thesis considers stochastic methods for large-scale linear systems, variational inequalities, and convex optimization problems. I focus on special structures that lend themselves to sampling, such as when the linear/nonlinear mapping or the objective function is an expected value or is the sum of a large number of terms, and/or the constraint is the intersection of a large number of simple...

Sequential Optimality Conditions and Variational Inequalities

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

A Projection-type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, cl...