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Your search keyword '"R. Blake Rector"' showing total 2 results
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2 results on '"R. Blake Rector"'

1. Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering

Author

Nguyen Mau Nam, Daniel Giles, and R. Blake Rector

Subjects
Convex hull, Convex analysis, Mathematical optimization, 021103 operations research, Control and Optimization, Applied Mathematics, Random coordinate descent, 010102 general mathematics, 0211 other engineering and technologies, Proper convex function, 02 engineering and technology, Subderivative, Management Science and Operations Research, 01 natural sciences, Convex optimization, Convex combination, 0101 mathematics, Conic optimization, Mathematics
Abstract

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 introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.

Published
2017

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

Author

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

Subjects
Control and Optimization, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, Management Science and Operations Research, 01 natural sciences, Combinatorics, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, FOS: Mathematics, Applied mathematics, 0101 mathematics, Mathematics - Optimization and Control, Finite set, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, 021103 operations research, Applied Mathematics, Exponential smoothing, Optimization and Control (math.OC), Theory of computation, Smallest-circle problem, Convex function, Sylvester equation, Gradient method, Smoothing, MathematicsofComputing_DISCRETEMATHEMATICS
Abstract

The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses 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.

Published
2015

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