An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem
To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method w...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6692024 |
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| author | Ahmad Alhawarat Thoi Trung Nguyen Ramadan Sabra Zabidin Salleh |
| author_facet | Ahmad Alhawarat Thoi Trung Nguyen Ramadan Sabra Zabidin Salleh |
| author_sort | Ahmad Alhawarat |
| collection | DOAJ |
| description | To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time. |
| format | Article |
| id | doaj-art-78744b87104e406da6676f2182b23659 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-78744b87104e406da6676f2182b236592025-02-03T06:06:28ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66920246692024An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization ProblemAhmad Alhawarat0Thoi Trung Nguyen1Ramadan Sabra2Zabidin Salleh3Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, VietnamDivision of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, VietnamDepartment of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi ArabiaDepartment of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, MalaysiaTo find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.http://dx.doi.org/10.1155/2021/6692024 |
| spellingShingle | Ahmad Alhawarat Thoi Trung Nguyen Ramadan Sabra Zabidin Salleh An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem Journal of Mathematics |
| title | An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem |
| title_full | An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem |
| title_fullStr | An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem |
| title_full_unstemmed | An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem |
| title_short | An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem |
| title_sort | efficient modified azprp conjugate gradient method for large scale unconstrained optimization problem |
| url | http://dx.doi.org/10.1155/2021/6692024 |
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