Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

M. Farrokhiniya () and A. Barani ()
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M. Farrokhiniya: Lorestan University
A. Barani: Lorestan University

Journal of Global Optimization, 2020, vol. 77, issue 3, No 10, 685 pages

Abstract: Abstract We provide definitions for Fréchet $$\varepsilon $$ε-subdifferential and Fréchet $$\varepsilon $$ε-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.

Keywords: Fréchet $$\varepsilon $$ ε -subdifferential; Fréchet $$\varepsilon $$ ε -normals set; Limiting subdifferential; Limiting normal cone; Perturbed distance function; Riemannian manifolds; 58C99; 58C05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-020-00889-w

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