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Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

Author

Listed:
  • M. Farrokhiniya

    (Lorestan University)

  • A. Barani

    (Lorestan University)

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.

Suggested Citation

  • M. Farrokhiniya & A. Barani, 2020. "Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds," Journal of Global Optimization, Springer, vol. 77(3), pages 661-685, July.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:3:d:10.1007_s10898-020-00889-w
    DOI: 10.1007/s10898-020-00889-w
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    References listed on IDEAS

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    1. Jin-Hua Wang & Chong Li & Hong-Kun Xu, 2010. "Subdifferentials of perturbed distance functions in Banach spaces," Journal of Global Optimization, Springer, vol. 46(4), pages 489-501, April.
    2. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    4. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
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