Convergence of a Proximal Point Algorithm for Solving Minimization Problems
We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradie...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/142862 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567986132615168 |
|---|---|
| author | Abdelouahed Hamdi M. A. Noor A. A. Mukheimer |
| author_facet | Abdelouahed Hamdi M. A. Noor A. A. Mukheimer |
| author_sort | Abdelouahed Hamdi |
| collection | DOAJ |
| description | We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones. |
| format | Article |
| id | doaj-art-220854416f8c4fcb8b1a998617fd5ac7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-220854416f8c4fcb8b1a998617fd5ac72025-02-03T00:59:53ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/142862142862Convergence of a Proximal Point Algorithm for Solving Minimization ProblemsAbdelouahed Hamdi0M. A. Noor1A. A. Mukheimer2Department of Mathematics, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaMathematics Department, COMSATS Institute of Information Technology, Islamabad, PakistanDepartment of Mathematics, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaWe introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones.http://dx.doi.org/10.1155/2012/142862 |
| spellingShingle | Abdelouahed Hamdi M. A. Noor A. A. Mukheimer Convergence of a Proximal Point Algorithm for Solving Minimization Problems Journal of Applied Mathematics |
| title | Convergence of a Proximal Point Algorithm for Solving Minimization Problems |
| title_full | Convergence of a Proximal Point Algorithm for Solving Minimization Problems |
| title_fullStr | Convergence of a Proximal Point Algorithm for Solving Minimization Problems |
| title_full_unstemmed | Convergence of a Proximal Point Algorithm for Solving Minimization Problems |
| title_short | Convergence of a Proximal Point Algorithm for Solving Minimization Problems |
| title_sort | convergence of a proximal point algorithm for solving minimization problems |
| url | http://dx.doi.org/10.1155/2012/142862 |
| work_keys_str_mv | AT abdelouahedhamdi convergenceofaproximalpointalgorithmforsolvingminimizationproblems AT manoor convergenceofaproximalpointalgorithmforsolvingminimizationproblems AT aamukheimer convergenceofaproximalpointalgorithmforsolvingminimizationproblems |