In this paper we present a bundle method for solving a generalized variational inequality problem. This problem consists in finding a zero of the sum of two multivalued operators defined on a real Hilbert space. The first one is monotone and the second one is the subdifferential of a lower semicontinuous proper convex function. The method is based on the auxiliary problem principle due to Cohen and the strategy is to approximate, in the subproblems, the nonsmooth convex function by a sequence of convex piecewise linear functions as in the bundle method in nonsmooth optimization.
Report 2001/04, Department of Mathematics, University of Namur, Belgium, March 2001