Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems
We present algorithms for solving a number of new models of facility location which generalize the classical Fermat–Torricelli problem. Our first approach involves using Nesterov’s smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Society for Industrial and Applied Mathematics
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/2852 |
| _version_ | 1848744067281715200 |
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| author | Nam, N.M. An, N.T. Rector, B. Sun, Jie |
| author_facet | Nam, N.M. An, N.T. Rector, B. Sun, Jie |
| author_sort | Nam, N.M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We present algorithms for solving a number of new models of facility location which generalize the classical Fermat–Torricelli problem. Our first approach involves using Nesterov’s smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms. |
| first_indexed | 2025-11-14T05:55:34Z |
| format | Journal Article |
| id | curtin-20.500.11937-2852 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:55:34Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-28522017-09-13T14:31:37Z Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems Nam, N.M. An, N.T. Rector, B. Sun, Jie MM principle Nesterov’s smoothing technique generalized Fermat–Torricelli problem subgradient-type algorithms Nesterov’s accelerated gradient - method We present algorithms for solving a number of new models of facility location which generalize the classical Fermat–Torricelli problem. Our first approach involves using Nesterov’s smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms. 2014 Journal Article http://hdl.handle.net/20.500.11937/2852 10.1137/130945442 Society for Industrial and Applied Mathematics fulltext |
| spellingShingle | MM principle Nesterov’s smoothing technique generalized Fermat–Torricelli problem subgradient-type algorithms Nesterov’s accelerated gradient - method Nam, N.M. An, N.T. Rector, B. Sun, Jie Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title | Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title_full | Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title_fullStr | Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title_full_unstemmed | Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title_short | Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems |
| title_sort | nonsmooth algorithms and nesterov’s smoothing technique for generalized fermat–torricelli problems |
| topic | MM principle Nesterov’s smoothing technique generalized Fermat–Torricelli problem subgradient-type algorithms Nesterov’s accelerated gradient - method |
| url | http://hdl.handle.net/20.500.11937/2852 |