Abstract

A proof is provided for the union of uniform closed balls conjecture introduced in a previous paper of the authors ["Proximal smoothness and the exterior sphere condition", J. Convex Analysis 16 (2009) 501–514]; see also C. Nour, R. J. Stern and J. Takche, "The union of uniform closed balls conjecture", Control and Cybernetics 38 (2009) 1525–1534, and "Generalized exterior sphere conditions and φ-convexity", Discrete and Continuous Dynamical Systems, Serie B (to appear). We also provide a generalization of this conjecture to the variable radius case.

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, Lebanon

cnour@lau.edu.lb

Ron J. Stern

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

stern@mathstat.concordia.ca

Jean Takche

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

jtakchi@lau.edu.lb

Keywords

  • Interior and exterior sphere conditions
  • union of uniform closed balls property
  • proximal analysis
  • nonsmooth analysis

References

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Suggested citation

C. Nour, R. J. Stern, J. Takche. “Validity of the Union of Uniform Closed Balls Conjecture.” Journal of Convex Analysis 18 (2011), No. 2, 589–600. https://doi.org/10.68381/jca18037

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.