Article ID: | iaor20128232 |
Volume: | 155 |
Issue: | 3 |
Start Page Number: | 902 |
End Page Number: | 922 |
Publication Date: | Dec 2012 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Langenberg Nils |
Keywords: | proximal point algorithm, Nash equilibrium |
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.