A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations
We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other wo...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/750834 |
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| _version_ | 1832545633692549120 |
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| author | Hamid Reza Erfanian M. H. Noori Skandari A. V. Kamyad |
| author_facet | Hamid Reza Erfanian M. H. Noori Skandari A. V. Kamyad |
| author_sort | Hamid Reza Erfanian |
| collection | DOAJ |
| description | We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented. |
| format | Article |
| id | doaj-art-3223ac5e09664dccacd8b0709f9046c2 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3223ac5e09664dccacd8b0709f9046c22025-02-03T07:25:09ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/750834750834A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth EquationsHamid Reza Erfanian0M. H. Noori Skandari1A. V. Kamyad2Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, IranDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, IranDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, IranWe present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.http://dx.doi.org/10.1155/2013/750834 |
| spellingShingle | Hamid Reza Erfanian M. H. Noori Skandari A. V. Kamyad A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations Journal of Mathematics |
| title | A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations |
| title_full | A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations |
| title_fullStr | A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations |
| title_full_unstemmed | A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations |
| title_short | A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations |
| title_sort | novel approach for solving nonsmooth optimization problems with application to nonsmooth equations |
| url | http://dx.doi.org/10.1155/2013/750834 |
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