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Limiting behavior of the approximate second-order subdifferential of a convex function

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Abstract

Hiriart-Urruty and the author recently introduced the notions of Dupin indicatrices for nonsmooth convex surfaces and studied them in connection with their concept of a second-order subdifferential for convex functions. They noticed that second-order subdifferentials can be viewed as limit sets of difference quotients involving approximate subdifferentials. In this paper, we elaborate this point in a more detailed way and discuss some related questions.

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The author is grateful to the referees for their helpful comments.

Communicated by A. V. Fiacco

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Seeger, A. Limiting behavior of the approximate second-order subdifferential of a convex function. J Optim Theory Appl 74, 527–544 (1992). https://doi.org/10.1007/BF00940325

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Key Words

  • Approximate subdifferential
  • second-order subdifferential
  • convex functions
  • Legendre-Fenchel transform
  • epiconvergence