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A new type of descent conjugate gradient method with exact line search

AIP Conference Proceedings 2016年第1期1739卷

作者： Nurul Hajar Mustafa Mamat Mohd. Rivaie Ibrahim Jusoh 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi MARA (UiTM) Terengganu Malaysia

Nowadays, conjugate gradient (CG) methods are impressive for solving nonlinear unconstrained optimization problems. In this paper, a new CG method is proposed and analyzed. This new CG method satisfies descent condition and its global convergence is established using exact line search. Numerical results show that this new CG method substantially outperforms the previous CG methods. This new CG method is considered robust, efficient and provided faster and stable convergence.

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A new steepest descent method with global convergence properties

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AIP Conference Proceedings 2016年第1期1739卷

作者： Zubai’ah Zainal Abidin Mustafa Mamat Mohd. Rivaie 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi Mara (UiTM) Terengganu Malaysia

One of the earliest and the best method to minimize a function is the classical steepest descent (SD) method. In this paper, a new modification of SD method is suggested using a new search direction, d k. The numerical results are presented based on number of iterations and CPU time. It shows that the new d k are efficient when compared to the classical SD.

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A modification of classical conjugate gradient method using strong Wolfe line search

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AIP Conference Proceedings 2016年第1期1739卷

作者： Syazni Shoid Mohd. Rivaie Mustafa Mamat 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi MARA (UiTM) Terengganu Malaysia

Recently many researches try to develop and improve the Conjugate Gradient (CG) methods because of its convergence properties and low computation costing. In this paper, another CG coefficient (βk) will be proposed which is categorized as modification in such a way to improve the performance of the classical CG methods. This paper is focused on generating βk with several desirable properties: (1) generate descent search direction at each iterations; and (2) converge globally by using strong Wolfe line search. Numerical comparisons of three CG methods show the robustness and the efficiency of the new method in solving all given problems.

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A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

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AIP Conference Proceedings 2016年第1期1787卷

作者： Nurul ‘Aini Mohd Rivaie Mustafa Mamat 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi MARA (UiTM) Terengganu Malaysia

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

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A spectral KRMI conjugate gradient method under the strong-Wolfe line search

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AIP Conference Proceedings 2016年第1期1739卷

作者： Wan Khadijah Mohd. Rivaie Mustafa Mamat Ibrahim Jusoh 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi MARA (UiTM) Terengganu Malaysia

In this paper, a modification of spectral conjugate gradient (CG) method is proposed which combines the advantages of the spectral CG method and the RMIL method namely as spectral Khadijah-Rivaie-Mustafa-Ibrahim (SKRMI) to solve unconstrained optimization problems. Based on inexact line searches, the objective function generates a sufficient descent direction and the global convergence property for the proposed method has been proved. Moreover, the method reduces to the standard RMIL method if exact line search is applied. Numerical results are also presented to examine the efficiency of the proposed method.

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A modified form of conjugate gradient method for unconstrained optimization problems

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AIP Conference Proceedings 2016年第1期1739卷

作者： Nur Hamizah Abdul Ghani Mohd. Rivaie Mustafa Mamat 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (UniSZA) Terengganu Malaysia 2Department of Computer Science and Mathematics Universiti Teknologi Mara (UiTM) Terengganu Malaysia

Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947–951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.

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Solving a large scale nonlinear unconstrained optimization with exact line search direction by using new coefficient of conjugate gradient methods

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AIP Conference Proceedings 2016年第1期1787卷

作者： Nur Syarafina Mohamed Mustafa Mamat Mohd Rivaie 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (Unisza) Campus Tembila Besut Terengganu Malaysia 2Department of Computer Sciences and Mathematics Universiti Teknologi MARA (UiTM) Terengganu Malaysia

Conjugate gradient (CG) methods are one of the tools in optimization. Due to its low computational memory requirement, this method is used in solving several of nonlinear unconstrained optimization problems from designs, economics, physics and engineering. In this paper, a new modification of CG family coefficient (βk) is proposed and posses global convergence under exact line search direction. Numerical experimental results based on the number of iterations and central processing unit (CPU) time show that the new βk performs better than some other well known CG methods under some standard test functions.

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The ADM solution of MHD non-Newtonian fluid with transient flow and heat transfer

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AIP Conference Proceedings 2016年第1期1775卷

作者： Qayyum Shah Mustafa Bin Mamat Taza Gul Novan Tofany 1Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Malaysia 2Department of Mathematics City University of Science and Information Technology KP Peshawar Pakistan 3Higher education Department GSSC KP Peshawar Pakistan 4Institute of Oceanography and Environment Universiti Malaysia Terangganu Malaysia

The present study deals with the time dependent motion of magneto-hydrodynamics (MHD) flow of a third grade fluid model with heat transfer. The fluid motion is studied in a porous medium between two inclined and periodically oscillating plates. The governing equations are modeled in the form of nonlinear partial differential equations. The modeled problems are then solved with the help of ADM technique. The physical features of the non-Newtonian fluid model and temperature distribution are presented and discussed the effect of imbedded parameter like local Stock number St, non dimensional variables α, γ1, γ2, γ3, γ4, γ5, γ6 and third grade non-Newtonian parameter β is the non-Newtonian parameter during vibratory motion of fluid flow in a porous medium is the main feature of this work.

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