On maximality of quasimonotone operators

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We introduce the notion of quasimonotone polar of a multivalued operator, in a similar way as the well-known monotone polar due to Martínez-Legaz and Svaiter. We first recover several properties similar to the monotone polar, including a characterization in terms of normal cones. Next, we use it to analyze certain aspects of maximal (in the sense of graph inclusion) quasimonotonicity, and its relation to the notion of maximal quasimonotonicity introduced by Aussel and Eberhard. Furthermore, we study the connections between quasimonotonicity and Minty Variational Inequality Problems and, in particular, we consider the general minimization problem. We conclude by characterizing the maximal quasimonotonicity of operators defined in the real line.
Original languageEnglish
Pages (from-to)87-101
Number of pages15
JournalSet-Valued and Variational Analysis
Issue number1
Early online date24 May 2017
StatePublished - 15 Mar 2019

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media Dordrecht.


  • Adjusted normal cones
  • Maximal quasimonotone operators
  • Minimization problem
  • Minty variational inequality
  • Quasimonotone operators
  • Quasimonotone polarity


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