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Full-Text Articles in Algebraic Geometry
The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, N. T. An, Daniel J. Giles, Nguyen Mau Nam, R. Blake Rector
The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, N. T. An, Daniel J. Giles, Nguyen Mau Nam, R. Blake Rector
Mathematics and Statistics Faculty Publications and Presentations
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.
Minimizing Differences Of Convex Functions With Applications To Facility Location And Clustering, Mau Nam Nguyen, R. Blake Rector, Daniel J. Giles
Minimizing Differences Of Convex Functions With Applications To Facility Location And Clustering, Mau Nam Nguyen, R. Blake Rector, Daniel J. Giles
Mathematics and Statistics Faculty Publications and Presentations
In this paper we develop algorithms to solve generalized Fermat-Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.