An Interior Proximal Method for a Class of Quasimonotone Variational Inequalities

Nils Langenberg ()
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Nils Langenberg: University of Trier

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 3, No 9, 902-922

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0111-9

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