Abstract

The Fréchet derivative of the Fenchel conjugate of the antidistance function is locally Lipschitz in the Hilbert space setting. It is shown that the Gâteaux differential of the operator, at points of the existence, is bounded self-adjoint operator (it is symmetric everywhere defined on the Hilbert space). Assuming Gâteaux or Fréchet differentiability of the operator results on the strong convergence of subgradients along some arcs are also provided.

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Keywords

  • Antidistance function
  • subdifferentials
  • subgradients
  • Gâteaux derivative
  • Fréchet derivative

Mathematics Subject Classification

49J52

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Suggested citation

D. Zagrodny. “Properties of the Fréchet Derivative of the Fenchel Conjugate of the Antidistance Function.” Journal of Convex Analysis 30 (2023), No. 4, 1351–1378. https://doi.org/10.68381/jca30061

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press LLC.