A Bundle Method to Solve Multivalued Variational Inequalities

Genevieve SALMON (Genevieve.Salmonfundp.ac.be)
Jean-Jacques STRODIOT (Jean-Jacques.Strodiotfundp.ac.be)
Van Hien NGUYEN (vhnguyenfundp.ac.be)

Abstract: 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.

Keywords: generalized variational inequality, auxiliary problem principle, bundle method

Category 1: Convex and Nonsmooth Optimization

Category 2: Complementarity and Variational Inequalities

Citation: Report 2001/04, Department of Mathematics, University of Namur, Belgium, March 2001

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Entry Submitted: 03/09/2001
Entry Accepted: 03/09/2001
Entry Last Modified: 03/09/2001

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