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Partitionable Mixed Variational Inequalities

  • E. Allevi
  • A. Gnudi
  • I. V. Konnov
  • E. O. Mazurkevich
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)

Abstract

Two recent papers [1] and [2] have presented existence and uniqueness results for solutions of mixed variational inequality problems involving P-mappings and convex and separable but not necessarily differentiable functions where the feasible set is defined by box type constraints. In this paper we generalise these results for the case where the subspaces constituting the initial space are not real lines.

Key words

Mixed variational inequalities nondifferentiable functions product sets order monotonicity existence and uniqueness results 

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References

  1. [1]
    I.V. Konnov, Properties of gap functions for mixed variational inequalities, Siberian Journal of Numerical Mathematics, 3 (2000), 259–270.zbMATHGoogle Scholar
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    I.V. Konnov and E.O. Volotskaya, Mixed variational inequalities and ecomonic equilibrium problems, Journal of Applied Mathematics, 6 (2002), 289–314.CrossRefMathSciNetGoogle Scholar
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    J.J. Moré, Classes of functions and feasibility conditions in nonlinear complementarity problems, Mathematical Programming, 6 (1974), 327–338.zbMATHCrossRefMathSciNetGoogle Scholar
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    C. Kanzow and M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Mathematical Programming, 83 (1998), 55–87.CrossRefMathSciNetGoogle Scholar
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    F. Facchinei and J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag, Berlin, 2003 (two volumes).Google Scholar
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    R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, (1970).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • E. Allevi
    • 1
  • A. Gnudi
    • 1
  • I. V. Konnov
    • 2
  • E. O. Mazurkevich
    • 2
  1. 1.Dept. of Mathematics, Statistics, Computer Science and ApplicationsBergamo UniversityBergamoItaly
  2. 2.Dept. of Applied MathematicsKazan UniversityKazanRussia

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