Journal of Engineering and Applied Sciences

Year: 2017
Volume: 12
Issue: 18
Page No. 4627 - 4631

Hybrid Quasi-Newton and Conjugate Gradient Method for Solving Unconstrained Optimization Problems

Authors : Nurul Aini, Nurul Hajar, Mustafa Mamat, Norhaslinda Zull and Mohd Rivaie

References

Andrei, N., 2008. An unconstrained optimization test functions collection. Adv. Mod. Optimiz., 10: 147-161.
Direct Link  |  

Armijo, L., 1966. Minimization of functions having lipschitz continuous first partial derivatives. Pac. J. Math., 16: 1-3.
CrossRef  |  Direct Link  |  

Broyden, C.G., J.E. Dennis and J.J. More, 1973. On the local and superlinear convergence of quasi-Newton methods. IMA. J. Appl. Math., 12: 223-245.
Direct Link  |  

Byrd, R.H. and J. Nocedal, 1989. A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM J. Numer. Anal., 26: 727-739.
CrossRef  |  

Dolan, E.D. and J.J. More, 2002. Benchmarking optimization software with performance profiles. Math. Program., 91: 201-213.
CrossRef  |  Direct Link  |  

Du, X.W., L.Q. Ye and C.X. Xu, 2001. Global convergence of a class of unconstrained optimal methods include the conjugate descent method. J. Eng. Math., 18: 120-122.

Fletcher, R. and C.M. Reeves, 1964. Function minimization by conjugate gradients. Comput. J., 7: 149-154.
CrossRef  |  Direct Link  |  

Fletcher, R., 1987. Practical Method of Optimization, Unconstrained Optimization. John Wiley & Sons, New York, USA., ISBN:9780471915478, Pages: 436.

Han, L. and M. Neumann, 2003. Combining quasi-Newton and steepest descent directions. Intl. J. Appl. Math., 12: 167-171.

Hery, M.A., M. Ibrahim and L.W. June, 2014. BFGS method: A new search direction. Sains Malaysiana, 43: 1591-1597.
Direct Link  |  

Hilstrom, K.E., 1977. A simulation test approach to the evaluation of nonlinear optimization algorithms. ACM Trans. Mathe. Software, 3: 305-315.
Direct Link  |  

Ibrahim, M.A.H., M. Mamat and W.J. Leong, 2014. The hybrid BFGS-CG method in solving unconstrained optimization problems. Abstract Appl. Anal., 2014: 1-6.
Direct Link  |  

Jaafar, R., M. Mamat and I. Mohd, 2013. A new scaled hybrid modified BFGS algorithms for unconstrained optimization. Appl. Math. Sci., 7: 263-270.

Jamil, M. and X.S. Yang, 2013. A literature survey of benchmark functions for global optimisation problems. Intl. J. Math. Modell. Numer. Optimisation, 4: 150-194.
CrossRef  |  Direct Link  |  

Ludwig, A., 2007. The Gauss-Seidel-quasi-Newton method: A hybrid algorithm for solving dynamic economic models. J. Econ. Dyn. Control, 31: 1610-1632.
Direct Link  |  

Luo, Y.Z., G.J. Tang and L.N. Zhou, 2008. Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method. Appl. Soft Comput., 8: 1068-1073.
Direct Link  |  

Mamat, M., I. Mohd, L.W. June and Y. Dasril, 2009. Hybrid broyden method for unconstrained optimization. Intl. J. Numer. Methods Appl., 1: 121-130.

Rivaie, M., M. Mamat, L.W. June and I. Mohd, 2012. A new class of nonlinear conjugate gradient coefficients with global convergence properties. Appl. Math. Comput., 218: 11323-11332.
Direct Link  |  

Sofi, A.Z.M., M. Mamat and I. Mohd, 2013. An improved BFGS search direction using exact line search for solving unconstrained optimization problems. Appl. Math. Sci., 7: 73-85.
Direct Link  |  

Sofi, M.A.Z., M. Mamat, I. Mohd and Y. Dasril, 2008. An alternative hybrid search direction for unconstrained optimization. J. Interdiscip. Math., 11: 731-739.
Direct Link  |  

Sun, W. and Y.X. Yuan, 2006. Optimization Theory and Methods: Nonlinear Programming. Springer-Verlag, New York, USA., ISBN-10: 0387249753, pp: 687.

Yuhong, D. and Y. Yaxiang, 1996. Convergence properties of the conjugate descent method. Adv. Math., 25: 552-562.

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