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Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

Abstract

We provide definitions for Fréchet \(\varepsilon \)-subdifferential and Fréchet \(\varepsilon \)-normals set for functions and sets in the Riemannian manifolds. Then we generalize the notions of Mordukhovich sequential subdifferential and normal cone (limiting subdifferential and normal cone) and develop several calculus rules for subdifferentials and normal cones in this setting. Finally, as an application, the limiting subdifferential of perturbed distance function is investigated in the Riemannian manifolds setting.

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Correspondence to A. Barani.

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Farrokhiniya, M., Barani, A. Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds. J Glob Optim (2020). https://doi.org/10.1007/s10898-020-00889-w

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Keywords

  • Fréchet \(\varepsilon \)-subdifferential
  • Fréchet \(\varepsilon \)-normals set
  • Limiting subdifferential
  • Limiting normal cone
  • Perturbed distance function
  • Riemannian manifolds

Mathematics Subject Classification

  • 58C99
  • 58C05