Journal of Convex Analysis 25 (2018), No. 1, 001--019
Copyright Heldermann Verlag 2018
Regularization via Sets Satisfying the Interior Sphere Condition
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
For a given closed subset S of Rn, 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.
Keywords: Regularization of sets, interior sphere condition, phi-convexity, Pompeiu-Hausdorff convergence, nonsmooth analysis.
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