Improving the performance of conjugate gradient method in solving unconstrained optimization problems and its application

The conjugate gradient (CO) method is the best in iterative methods due to its simple algorithm, low memory storage, and good convergence analysis. However, a major problem of the existing CO methods is that it can be very slow on the certain type of unconstrained optimization problems. Therefore, t...

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Bibliographic Details
Main Author: Nur Hamizah Abdul Ghani (Author)
Corporate Author: Universiti Sultan Zainal Abidin . Faculty of Informatics and Computing
Format: Thesis Book
Language:English
Subjects:

MARC

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090 0 0 |a QA218   |b .N874 2017 
100 0 |a Nur Hamizah Abdul Ghani ,   |e author 
245 1 0 |a Improving the performance of conjugate gradient method in solving unconstrained optimization problems and its application   |c Nur Hamizah Binti Abdul Ghani 
264 0 |c 2017 
300 |a xvii, 227 pages :   |b illustrations(some colour) ;   |c 31 cm. 
336 |a text  |2 rdacontent 
337 |a unmediated  |2 rdamedia 
338 |a volume  |2 rdacarrier 
502 |a Thesis (Degree of doctor of philosophy) - Universiti Sultan Zainal Abidin, 2017 
504 |a Includes bibliographical references (leaves 170-179) 
505 1 |a 1. Introduction of the research -- 2. Literature review -- 3. Conjugate gradient method -- 4. Development of conjugate gradient methods -- 5. Numerical result and discussion -- 6. Implementation of new cg methods on corruption perception index in Malaysia -- 7. Conclusion and reccomendations 
520 |a The conjugate gradient (CO) method is the best in iterative methods due to its simple algorithm, low memory storage, and good convergence analysis. However, a major problem of the existing CO methods is that it can be very slow on the certain type of unconstrained optimization problems. Therefore, there is needed to improve the efficiency of those methods based on the number of iterations and central processing times per unit. This research proposes two new CO methods as NRM and NRM 1 methods, based on the researcher's name (Nur Hamizah, Rivaie and Mustafa) and classified into the groups of classical and hybrid CO methods, respectively. Both approaches are tested based on the exact and inexact line search. Theoretical proofs are shown that both new CO methods pos ess the sufficient descent and global convergence properties. The efficiency of the new CO methods are studied by testing on 30 standard test problems of unconstrained optimization functions, with a total of 109 problems based on four different initial points ranging from small dimensions to large dimensions problems utilizing MatlabR2012 programming. The NRM and NRM 1 methods are compared with the existing CO methods, which are Hestenes¬Stiefel (HS), Rivaie-Mustafa-I mail-Leong (RMIL), Touati-Ahmed-Storey (TS) and Jinbao-Han-Jiang (JHJ). Comparison based on performance profile shows that both new CO methods are efficient in their cla s of CO. From the exact line search, the NRM I method shows the highest successful percentage to solve test functions in group of hybrid CO compared to TS and JHJ methods. Meanwhile in group of classical CO, the NRM and RMIL method show the same highest successful percentage to solve the test functions. From the inexact line search, the NRM 1 and NRM methods show the highest successful percentage to solve test functions compared to the TS, JHJ, HS and RMIL methods. Both new methods are able to lessen the number of iterations and central processing times per unit. Moreover, the performance of CO methods in inexact line search is better than the performance in exact line search. Besides that, the numerical result also shows that new CO methods have capability to be applied in regression analysis problem. Thus, both of the new methods show promising results to be implemented in further study. 
610 2 0 |a Universiti Sultan Zainal Abidin   |x Dissertations 
610 2 0 |a Universiti Sultan Zainal Abidin   |x Faculty of Informatics and Computing   |v Dissertations 
650 0 |a Conjugate gradient methods 
655 0 |a Dissertations, Academic 
710 2 |a Universiti Sultan Zainal Abidin .   |b Faculty of Informatics and Computing 
999 |a 1000173185   |b Thesis   |c Reference   |e Tembila Campus