On a Primal-Dual Analytic Center Cutting Plane Method for VariationalInequalities

Authors:
M. Denault;J. -L. Goffin
Affiliations:
GERAD, McGill University, Montréal Québec, Canada;GERAD, McGill University, Montréal Québec, Canada. jlg@crt.umontreal.ca
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Year:
1999

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Abstract

We present an algorithm for variational inequalities VI({\cal F}, Y)that uses a primal-dual version of the Analytic Center Cutting PlaneMethod.The point-to-set mapping {\cal F} is assumed to be monotone, orpseudomonotone. Each computation of a new analytic center requiresat most four Newton iterations, in theory, and in practiceone or sometimes two. Linear equalities that may be included in the definitionof the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequalityproblems as well as on one where the functional results from thesolution of large subproblems. The method is robust and competitive withalgorithms which use the same information as this one.