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Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

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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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Authors and Affiliations

  1. Department of Mathematics, Lorestan University, P. O. Box 465, Khoramabad, Iran

    M. Farrokhiniya & A. Barani

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  1. M. Farrokhiniya
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  2. A. Barani
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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 77, 661–685 (2020). https://doi.org/10.1007/s10898-020-00889-w

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