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The Log-Exponential Smoothing Technique and Nesterov’s Accelerated Gradient Method for Generalized Sylvester Problems

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Listed:
  • Nguyen Thai An

    (Thua Thien Hue College of Education)

  • Daniel Giles

    (Portland State University)

  • Nguyen Mau Nam

    (Portland State University)

  • R. Blake Rector

    (Portland State University)

Abstract

The Sylvester or smallest enclosing circle problem involves finding the smallest circle enclosing a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these problems.

Suggested Citation

  • Nguyen Thai An & Daniel Giles & Nguyen Mau Nam & R. Blake Rector, 2016. "The Log-Exponential Smoothing Technique and Nesterov’s Accelerated Gradient Method for Generalized Sylvester Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 559-583, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0811-z
    DOI: 10.1007/s10957-015-0811-z
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    References listed on IDEAS

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    1. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    2. Thomas Jahn & Yaakov S. Kupitz & Horst Martini & Christian Richter, 2015. "Minsum Location Extended to Gauges and to Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 711-746, September.
    3. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.

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