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Maximal quasimonotonicity and dense single-directional properties of quasimonotone operators

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Abstract

The concept of maximal quasimonotonicity of set-valued map is introduced and studied. Regularity properties of this class of operators is investigated, in particular the ccvc property, an adaptation to the quasimonotone case of the classical notion of cusco map. In an Asplund space, we provide sufficient conditions for a ccvc quasimonotone operator to be single-directional on a \(G_\delta \)-dense subset.

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Authors and Affiliations

  1. Lab. PROMES, UPR CNRS 8521, University of Perpignan, Perpignan, France

    D. Aussel

  2. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, 3001, Australia

    A. Eberhard

Authors
  1. D. Aussel
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  2. A. Eberhard
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Correspondence to D. Aussel.

Additional information

The research of the second author was supported by the ARC Discovery grant no. DP0987445.

Dedicated to Jonathan Borwein on the occassion of his 60th birthday.

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Aussel, D., Eberhard, A. Maximal quasimonotonicity and dense single-directional properties of quasimonotone operators. Math. Program. 139, 27–54 (2013). https://doi.org/10.1007/s10107-013-0658-8

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Keywords

Mathematics Subject Classification (2000)