Abstract

The concepts of φ-convexity and prox-regularity for sets are studied in the framework of finite-dimensional Riemannian manifolds. We prove that the two concepts coincide and these sets are contained in the class of sets with the unique footpoint property. Then by using a characterization of elements of proximal normal cone, we show that under certain conditions a set with the unique footpoint property is a φ-convex set.

Author information

Contact details are reproduced from the original publication and may be historical.

Mohamad R. Pouryayevali

Department of Mathematics, University of Isfahan, Isfahan, Iran

pourya@math.ui.ac.ir

Keywords

  • Phi-convex sets
  • prox-regular sets
  • sets with the unique footpoint property
  • nonsmooth analysis
  • Riemannian manifolds

Mathematics Subject Classification

58C20, 58C06, 49J52

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Suggested citation

M. R. Pouryayevali, H. Radmanesh. “Sets with the Unique Footpoint Property and φ-Convex Subsets of Riemannian Manifolds.” Journal of Convex Analysis 26 (2019), No. 2, 617–633. https://doi.org/10.68381/jca26033

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press.