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Nonsmooth Algorithms and Nesterov’s Smoothing Techniques for Generalized Fermat-Torricelli Problems

Nguyen Mau Nam (mnn3***at***pdx.edu)
Thai An Nguyen (thaian2784***at***gmail.com)
R. Blake Rector (r.b.rector***at***pdx.edu)
Jie Sun (jsun***at***nus.edu.sg)

Abstract: In this paper we present some algorithms for solving a number of new models of facility location involving sets which generalize the classical Fermat-Torricelli problem. Our approach uses subgradient-type algorithms to cope with nondi erentiabilty of the distance functions therein. Another approach involves approximating nonsmooth optimization problems by smooth optimizations problems using Nesterov's smoothing techniques. Convergence of the algorithms are proved. Extensive numerical results are also presented to show the effectiveness of the proposed algorithms.

Keywords: Subgradient-type algorithms, MM Principle, Nesterov's accelerated gradient method, generalized Fermat-Torricelli problem

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 07/22/2013
Entry Accepted: 07/23/2013
Entry Last Modified: 05/07/2014

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