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

Nguyen Thai An (), Daniel Giles (), Nguyen Mau Nam () and R. Blake Rector ()
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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

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 10, 559-583

Abstract: 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.

Keywords: Log-exponential smoothing technique; Majorization minimization algorithm; Nesterov’s accelerated gradient method; Generalized Sylvester problem; Primary 49J52; 49J53; Secondary 90C30 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-015-0811-z

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