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Journal of Optimization Theory and Applications

, Volume 155, Issue 3, pp 902–922 | Cite as

An Interior Proximal Method for a Class of Quasimonotone Variational Inequalities

  • Nils Langenberg
Article

Abstract

The Bregman-function-based Proximal Point Algorithm for variational inequalities is studied. Classical papers on this method deal with the assumption that the operator of the variational inequality is monotone. Motivated by the fact that this assumption can be considered to be restrictive, e.g., in the discussion of Nash equilibrium problems, the main objective of the present paper is to provide a convergence analysis only using a weaker assumption called quasimonotonicity. To the best of our knowledge, this is the first algorithm established for this general and frequently studied class of problems.

Keywords

Quasimonotone operators Variational inequalities Bregman distances Proximal Point Algorithm Interior-point-effect 

Notes

Acknowledgements

I am grateful to an anonymous referee whose comments greatly improved the present paper. Moreover, my thanks also go to the associate editor and the editor-in-chief for further very helpful remarks.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TrierTrierGermany

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