Sponsor
The research of Daniel Giles was partially supported by the USA National Science Foundation under grant DMS-1411817. The research of Nguyen Mau Nam was partially supported by the USA National Science Foundation under grant DMS-1411817 and the Simons Foundation under grant #208785.
Document Type
Pre-Print
Publication Date
2-2016
Subjects
Sylvester matrix equations, Optimization (Mathematics), Algorithms, Convex functions
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.
DOI
10.1007/s10957-015-0811-z
Persistent Identifier
http://archives.pdx.edu/ds/psu/17809
Citation Details
An, N. T.; Giles, Daniel J.; Nam, Nguyen Mau; and Rector, R. Blake, "The Log-Exponential Smoothing Technique and Nesterov’s Accelerated Gradient Method for Generalized Sylvester Problems" (2016). Mathematics and Statistics Faculty Publications and Presentations. 155.
http://archives.pdx.edu/ds/psu/17809
Description
This is the pre-print version of a work that was accepted for publication in Journal of Optimization Theory and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Optimization Theory and Applications and can be found online at: http://dx.doi.org/10.1007/s10957-015-0811-z