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.
Sylvester matrix equations, Optimization (Mathematics), Algorithms, Convex functions
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.
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.