A logarithmic-quadratic proximal method for variational inequalities

A logarithmic-quadratic proximal method for variational inequalities

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Article ID: iaor20003635
Country: Netherlands
Volume: 12
Issue: 1/2/3
Start Page Number: 31
End Page Number: 40
Publication Date: Jan 1999
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: Proximal-like method
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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