An extended descent framework for variational inequalities

In this paper, we develop a very general descent framework for solving asymmetric, monotone variational inequalities. We introduce two classes of differentiable merit functions and the associated global convergence frameworks which include, as special instances, the projection, Newton, quasi-Newton, linear Jacobi, and nonlinear methods. The generic algorithm is very flexible and consequently well suited for exploiting any particular structure of the problem.This research was supported by the National Science and Engineering Research Council of Canada, Grant A5789, and by the Department of National Defence of Canada, Grant FUHBP.