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Visible Points in Convex Sets and Best Approximation

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Computational and Analytical Mathematics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

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Abstract

The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets are developed. In particular, it is shown that this concept is useful in the study of best approximation, and it also seems to have potential value in the study of robotics.

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References

  1. Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011)

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Acknowledgements

We are greatly indebted to Heinz Bauschke who proofread this paper and made several suggestions that greatly improved the final version. Zikatanov was supported in part by the National Science Foundation DMS-1217142 and Department of Energy DE-SC0006903.

Author information

Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, McAllister Building - MCL G5, University Park, PA, 16802, USA

    Frank Deutsch & Ludmil Zikatanov

  2. The Pennsylvania State University, 146 Cedar Ridge Drive, Port Matilda, PA, 16870, USA

    Hein Hundal

Authors
  1. Frank Deutsch
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  2. Hein Hundal
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  3. Ludmil Zikatanov
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Corresponding author

Correspondence to Frank Deutsch .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

Additional information

Dedicated to Jonathan Borwein on the occasion of his 60th birthday

Communicated by Heinz H. Bauschke.

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© 2013 Springer Science+Business Media New York

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Deutsch, F., Hundal, H., Zikatanov, L. (2013). Visible Points in Convex Sets and Best Approximation. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_15

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