A Logarithmic-Quadratic Proximal Method for Variational Inequalities

Authors:
Alfred Auslender;Marc Teboulle;Sami Ben-Tiba
Affiliations:
Laboratoire d‘ Econometrie de L‘Ecole Polytechnique 1 Rue Descartes, Paris 75005, France. auslen@poly.polytechnic.fr;School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel. teboulle@math.tau.ac.il;Laboratoire d‘ Econometrie de L‘Ecole Polytechnique 1 Rue Descartes, Paris 75005, France. bentiba@poly.polytechnic.fr
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 a new method for solving variationalinequalities on polyhedra. The method is proximal based, butuses a very special logarithmic-quadratic proximal term whichreplaces the usual quadratic, and leads to an interior proximaltype algorithm. We allow for computing the iteratesapproximately and prove that the resulting method is globallyconvergent under the sole assumption that the optimal set of thevariational inequality is nonempty.