An improved Polak-Ribiere-Polyak method using strong wolfe-powell line search for unconstrained optimization problems
The unconstrained optimization problem has been dealing with different methods to be solved recently. The most common solution is the conjugate gradient (CG) method due to its convergence speed, simplicity, low memory requirements, and its capability to solve large-scale problems. There are many mod...
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| Format: | Thesis Book |
| Language: | English |
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| Summary: | The unconstrained optimization problem has been dealing with different methods to be solved recently. The most common solution is the conjugate gradient (CG) method due to its convergence speed, simplicity, low memory requirements, and its capability to solve large-scale problems. There are many modifications of the CG method with global convergence properties, however, some of them possess a high processing time when applying in real problems. Therefore, it is proposed new modifications that have global convergence properties and efficient compared to other CG methods. Besides, they can be used in practical applications. In this thesis, two improved methods of Polak- Ribi ere Polyak are proposed that are Dawahdeh, Mamat, and Rivaie (DMAR) method and Mahmoud, Mamat, and Rivaie (MMAR) method. The sufficient descent condition, as well as the global convergence of the proposed methods, are established under strong Wolfe-Powell (SWP) line search. Furthermore, the performance of these methods is tested using 33 standard benchmark test problems. Numerical results are analysed using the performance profile based on the number of iterations and the processing time. All the algorithms are coded in the Matlab subroutine and the finding is plotted using Sigma Plot software. The proposed methods are compared with the existing CG methods of Polak-Ribiere-Polyak plus (PRP+) , Wei, Yao, and Liu (WYL), new Polak-RibierePolyak (NPRP), and Aini, Rivaie, and Mustafa (ARM). The tests cover problems of a small scale to a large scale whereas the initial points are chosen around the solution point from the nearest to that furthest. The new CG methods are tested for applicability by using them to solve a function constructed from real data. DMAR and MMAR methods shown to have sufficient descent condition and possess global convergence properties. The result shows both methods have successfully solved 100 % the entire test problem under SWP line search compared to the methods ofPRP+, WYL, NPRP, and ARM with 68.50%, 99.10%, 98.80%, and 85.30% respectively. In addition, DMAR and MMAR methods have the least processing time. Based on the numerical results, they are superior to the other tested CG methods. Also, the proposed methods are proved to be applicable in a real case. The proposed CG methods possess global convergence properties and they are shown to be very efficient and robust compared to the other CG methods. Hence, the objectives achieved indicate that the proposed CG methods can be used as an alternative for solving large-scale unconstrained optimization problems. |
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| Item Description: | x |
| Physical Description: | xvii, 216 leaves; 31 cm. |
| Bibliography: | Includes bibliographical references (leaves 141-155) |
| ISBN: | x |