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Convex Analysis and Monotone Operator Theory in Hilbert Spaces pp 323–331Cite as

Stronger Notions of Monotonicity

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Part of the book series: CMS Books in Mathematics ((CMSBM))

Abstract

This chapter collects basic results on various stronger notions of monotonicity (para, strict, uniform, strong, and cyclic) and their relationships to properties of convex functions. A fundamental result is Rockafellar’s characterization of maximally cyclically monotone operators as subdifferential operators and a corresponding uniqueness result for the underlying convex function.

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Authors and Affiliations

  1. Mathematics Irving K. Barber School, University of British Columbia, Kelowna, B.C., V1V 1V7, Canada

    Heinz H. Bauschke

  2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, 4, Place Jussieu, 75005, Paris, France

    Patrick L. Combettes

Authors
  1. Heinz H. Bauschke
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  2. Patrick L. Combettes
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Correspondence to Heinz H. Bauschke .

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© 2011 Springer Science+Business Media, LLC

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Bauschke, H.H., Combettes, P.L. (2011). Stronger Notions of Monotonicity. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_22

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