Optimization Letters

, Volume 1, Issue 1, pp 21–32 | Cite as

Proximality and Chebyshev sets

  • Jonathan M. BorweinEmail author
Original Paper


This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.


Chebyshev sets Nonlinear analysis Convex analysis Variational analysis Proximal points Best approximation Farthest points 

1991 Mathematics Subject Classification

47H05 46N10 46A22 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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