Azfi Zaidi Mohammad Sofi
Universiti Malaysia Terengganu
MetaheuristicAlgorithmQuasi-Newton methodMulti-swarm optimizationMathematical optimizationBroyden–Fletcher–Goldfarb–Shanno algorithmOptimization problemMethod of steepest descentIterative methodQuadratic unconstrained binary optimizationHessian matrixDescent (mathematics)Applied mathematicsUnconstrained optimizationMathematicsNumerical analysisFunction (mathematics)L-reductionConvergence (routing)Broyden's methodConjugate gradient methodSelection (genetic algorithm)Line searchProperty (programming)Partial differential equationImage processing
Publications 7
In this article, a new search direction for the Broyden family method is proposed for solving unconstrained optimization problems. The new search direction is developed by using the search direction of conjugate gradient method approach. This method is popular as M-Broyden method. The suggested method has an attractive property that its search direction is sufficiently descent in every iteration. Under mild conditions, we prove that the proposed method has global convergence.
#3Leong Wah JuneH-Index: 4
Last. Azfi Zaidi Mohammad SofiH-Index: 2
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In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method ...
The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi-newton method for solving optimization problem is suggested. The Broyden family formula is used as an approximation of Hessian in the hybrid method and the quasi-Newton method. Our numerical analysis...
Quasi-Newton method is one of the most efficient and well known method for solving unconstrained optimization problems. In Quasi-Newton method, BFGS update is the finest Hessian update to work with. In this paper, an alternative algorithm for the BFGS update is proposed by changing the condition for the step size selection and we conclude the result analysis at the end of this paper by the number of the iteration and by the number of the function evaluation. Proven here that our proposed BFGS al...
Last. Wan Muhammad Amir Wan Ahmad (UMT: Universiti Malaysia Terengganu)H-Index: 1
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The Broyden family method for unconstrained optimization is known as one of the most efficient method in solving unconstrained optimization problem. Step size and search direction play the most important role to the convergence of the Broyden family method. Step size is proved to be successful method to solve the problem; however, it is definite to solve some complicated optimization problems. In this paper, we introduced the alternative procedure in determining the step size. This alternative p...
#1Azfi Zaidi Mohammad Sofi (UMT: Universiti Malaysia Terengganu)H-Index: 2
#2Mustafa Mamat (UMT: Universiti Malaysia Terengganu)H-Index: 16
Last. Yosza Dasril (UTeM: Universiti Teknikal Malaysia Melaka)H-Index: 5
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Abstract Quasi-Newton is one of the most popular iterative method for solving unconstrained optimization and recently, there are several researchers who work on hybrid quasi-Newton and steepest descent method and this method namely QN-SD. In this paper, we proposed an alternative search direction for this method and we proved its global convergence. Several standard optimization problems had been tested on this method and the result analysis was displayed at the end of this paper.
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