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Characterizations of relatively generalized monotone maps

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Abstract

New concepts of relative monotonicity were introduced in Konnov (Oper Res Lett 28:21–26, 2001a) which extend the usual ones. These concepts enable us to establish new existence and uniqueness results for variational inequality problems over product sets. This paper presents first-order characterizations of new (generalized) monotonicity concepts. Specialized results are obtained for the affine case.

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Authors and Affiliations

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

    E. Allevi

  2. Department of Mathematics, Statistics, Informatics and Applications, Bergamo University, Piazza Rosate, 2, Bergamo, 24129, Italy

    A. Gnudi

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

    I. V. Konnov

  4. A.G.Anderson Graduate School of Management, University of California, Riverside, CA, 92521, USA

    S. Schaible

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

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Allevi, E., Gnudi, A., Konnov, I.V. et al. Characterizations of relatively generalized monotone maps. Math Meth Oper Res 65, 293–303 (2007). https://doi.org/10.1007/s00186-006-0115-z

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  • DOI: https://doi.org/10.1007/s00186-006-0115-z

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