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The Proximal Point Method for Nonmonotone Variational Inequalities

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Abstract

We consider an application of the proximal point method to variational inequality problems subject to box constraints, whose cost mappings possess order monotonicity properties instead of the usual monotonicity ones. Usually, convergence results of such methods require the additional boundedness assumption of the solutions set. We suggest another approach to obtaining convergence results for proximal point methods which is based on the assumption that the dual variational inequality is solvable. Then the solutions set may be unbounded. We present classes of economic equilibrium problems which satisfy such assumptions.

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Authors and Affiliations

  1. Department of Quantitative Methods, Brescia University, Contrada Santa Chiara, 50, Brescia, 25122, Italy

    E. Allevi

  2. Department of Mathematics, Statistics, Informatics and Applications, Bergamo University, Via dei Caniana, 2, Bergamo, 24127, Italy

    A. Gnudi

  3. Department of Applied Mathematics, Kazan University, ul. Kremlevskaya,18, Kazan, 420008, Russia

    I. V. Konnov

Authors
  1. E. Allevi
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  2. A. Gnudi
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  3. I. V. Konnov
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Correspondence to I. V. Konnov.

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Allevi, E., Gnudi, A. & Konnov, I.V. The Proximal Point Method for Nonmonotone Variational Inequalities. Math Meth Oper Res 63, 553–565 (2006). https://doi.org/10.1007/s00186-005-0052-2

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  • DOI: https://doi.org/10.1007/s00186-005-0052-2

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