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A Logarithmic-Quadratic Proximal Method for Variational Inequalities |
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| Authors: | Alfred Auslender Marc Teboulle Sami Ben-Tiba |
| Affiliation: | (1) Laboratoire d' Econometrie de L'Ecole Polytechnique, 1 Rue Descartes, Paris, 75005, France;(2) School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978, Israel;(3) Laboratoire d' Econometrie de L'Ecole Polytechnique, 1 Rue Descartes, Paris, 75005, France |
| Abstract: | We present a new method for solving variational inequalities on polyhedra. The method is proximal based, but uses a very special logarithmic-quadratic proximal term which replaces the usual quadratic, and leads to an interior proximal type algorithm. We allow for computing the iterates approximately and prove that the resulting method is globally convergent under the sole assumption that the optimal set of the variational inequality is nonempty. |
| Keywords: | variational inequalities nonlinear complementarity proximal-like methods maximal monotone operators global convergence interior point methods saddle point computation |
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