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.
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Auslender, A., Teboulle, M. & Ben-Tiba, S. A Logarithmic-Quadratic Proximal Method for Variational Inequalities. Computational Optimization and Applications 12, 31–40 (1999). https://doi.org/10.1023/A:1008607511915
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DOI: https://doi.org/10.1023/A:1008607511915