A NEW COEFFICIENT OF CONJUGATE GRADIENT METHODS FOR NONLINEAR UNCONSTRAINED OPTIMIZATION
DOI:
https://doi.org/10.11113/jt.v78.8988Keywords:
Conjugate gradient method, conjugate gradient coefficient, exact line search, global convergence, and unconstrained optimizationAbstract
Conjugate gradient (CG) methods are widely used in solving nonlinear unconstrained optimization problems such as designs, economics, physics and engineering due to its low computational memory requirement. In this paper, a new modifications of CG coefficient ( ) which possessed global convergence properties is proposed by using exact line search. Based on the number of iterations and central processing unit (CPU) time, the numerical results show that the new  performs better than some other well known CG methods under some standard test functions.
References
Fletcher, R. and Reeves, C. 1964. Function Minimization By Conjugate Gradients. Computational Journal. 7: 149-154.
Polak, E. and Ribiere, G. 1969. Rev. Francaise Informat Recherche Operationelle. 3E Annee. 16: 35-43.
Hestenes, M.R. and Steifel, E. 1962. Method Of Conjugate Gradient For Solving Linear Equations. J. Res. Nat. Bur. Stand. 49: 409-436.
Dai, Y. H. and Yuan, Y. 2000. A Nonlinear Conjugate Gradient with Strong Global Convergence Properties. SIAM J. Optim. 10: 177-182.
Fletcher, R. 1987. Practical Methods Of Unconstrained Optimization. New York: J. Wiley and Sons.
Rivaie, Mamat M., June, M. L. W. and Mohd, I. 2012. A New Class Of Nonlinear Conjugate Gradient Coefficients With Global Convergence Properties. Applied Mathematics and Computation. 218: 11323-11332.
Dai, Y. H. and Yuan, Y. 1998. Nonlinear Conjugate Gradient Method. Beijing: Shanghai Scientific and Technical Publishers.
Yuan, Y. and Sun, W. 1999. Theory And Methods Of Optimization. Beijing: Science Press of China.
Narushima, Y. Yabe, H. and Ford, J. A. 2011. Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization. SIAM J. Optim. 21: 212-230.
Zoutendijk, G. 1970. Nonlinear programming computational methods. Abadie J. (Ed.). Integer and Nonlinear Programming. 37-86.
Dai, Y. H. and Yuan, Y. 2002. Modified Conjugate Gradient Method for Unconstrained Optimization. J. Compt. Appl. Math. 18(6): 575-582.
Hamoda, M. Rivaie, M. Mamat, M. Salleh, Z. and Amani, Z. 2015. A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization. Applied Mathematical Sciences. 9(37): 1813-1822.
Hajar, N. Mamat, M. Rivaie, M. and Salleh, Z. 2015. A Combination of Polak-Ribiere and Hestenes-Stiefel Coefficient in Conjugate Gradient Method for Unconstrained Optimization. Applied Mathematical Sciences. 9(63): 3131-3142.
Rivaie, M. Abashar, A. Mamat, M. Mohd, I. 2014. The Convergence Properties of a New a Type of Conjugate Gradient Methods. Applied Mathematical Sciences. 8(1): 33-34.
Zoutendijk, G. 1970. Nonlinear Programming Computational Methods. Abadie J. (Ed.). Ineteger and Nonlinear Programming. North Holland, Amsterdam.
Yuan, G. Lu, S. and Wei, Z. 2010. A Line Search Algorithm For Unconstrained Optimization. J. Soft. Eng. App. 3: 409-436.
More, J. J. Garbow, B. and Hillstrom, K. E. 1981. Testing Unconstrained Optimization Software. Journal ACM Transaction on Mathematical Software. 7(1): 17-41.
Hilstrom, K. E. 1977. A Simulation Test Approach To The Evaluation Of Nonlinear Optimization Algorithms. A.C.M. Trans. Maths. Softw. 3(4): 305-315.
Dolan, E. and More, J. J. 2002. Benchmarking Optimization Software With Performance Profile. Maths.Prog. 91(2): 201-213.
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