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Ubiquitous Subdifferentials, r L –density and Maximal Monotonicity

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Abstract

In this paper, we first investigate an abstract subdifferential for which (using Ekeland’s variational principle) we can prove an analog of the Brøndsted–Rockafellar property. We introduce the “ r L –density” of a subset of the product of a Banach space with its dual. A closed r L –dense monotone set is maximally monotone, but we will also consider the case of nonmonotone closed r L –dense sets. As a special case of our results, we can prove Rockafellar’s result that the subdifferential of a proper convex lower semicontinuous function is maximally monotone.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Stephen Simons

  2. Department of Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Xianfu Wang

Authors
  1. Stephen Simons
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  2. Xianfu Wang
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Correspondence to Stephen Simons.

Additional information

This paper is dedicated to Lionel Thibault, in recognition of his contribution to convex analysis and related fields

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Simons, S., Wang, X. Ubiquitous Subdifferentials, r L –density and Maximal Monotonicity. Set-Valued Var. Anal 23, 631–642 (2015). https://doi.org/10.1007/s11228-015-0326-7

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  • DOI: https://doi.org/10.1007/s11228-015-0326-7

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