Abstract

For a given closed subset S of Rn\mathbb{R}^n, we provide an inner approximation of S by sets satisfying the interior sphere condition. The fact that our approximation sets satisfy the interior sphere condition with variable radius, allows us to approach any corner and to use the Pompeiu-Hausdorff convergence even if the set S is unbounded.

Author information

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

Chadi Nour

Dept. of Computer Science and Mathematics, Lebanese American University, P.O. Box 36 - Byblos Campus, Byblos, Lebanon

cnour@lau.edu.lb

Hassan Saoud

Dept. of Mathematics, Lebanese University, Faculty of Sciences II, P.O. Box 90656, Fanar-Matn, Lebanon

hassan.saoud@ul.edu.lb

Jean Takche

Dept. of Computer Science and Mathematics, Lebanese American University, P.O. Box 36 - Byblos Campus, Byblos, Lebanon

jtakchi@lau.edu.lb

Keywords

  • Regularization of sets
  • interior sphere condition
  • phi-convexity
  • Pompeiu-Hausdorff convergence
  • nonsmooth analysis

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Suggested citation

C. Nour, H. Saoud, J. Takche. “Regularization via Sets Satisfying the Interior Sphere Condition.” Journal of Convex Analysis 25 (2018), No. 1, 1–19. https://doi.org/10.68381/jca25001

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.