New Proposed Conjugate Gradient Method for Nonlinear Unconstrained Optimization
Keywords:
Unconstrained Optimization, Conjugate Gradient Method, Homotopy TheoryAbstract
In this paper, we suggest a new conjugate gradient method for unconstrained optimization by using homotopy theory. Our suggestion algorithm satisfies the conjugacy and descent conditions. Numerical result shows that our new algorithm is better than the standard CG algorithm with respect to the NOI and NOF.
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References
Dai Y.H. and Yuan Y, (2001), New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optima. 43, 87–101.
Fletcher, R.,(1987). Practical Methods of Optimization, Vol I: Unconstrained Optimization. New York: Wiley.
Fletcher, R. and Reeves, C. (1964), Function minimization by conjugate gradients. J. Comput., 7, 149–154.
Hestenes, M.R. and Stiefel, E. L. ,(1952), Method of conjugate gradient for solving linear systems. J. Res. Natl.Bur. Stand., 49, 409–432.
Omar D. H., (2013), Numerical Methods for Unconstrained Optimization Algorithms with Chaos Theory , University of Zakho, Kurdistan Region-Iraq.
Polak,E. and Ribiere, G., (1969), Note surla convergence des methods' de directions conjugu´ ees. Rev. Fr.Imform. Rech. Op-er., 16, 35–43.
Watson L. T. and Haftka, (1988), Modern Homotopy Methods in Optimization, TR 88-51, Virginia Polytechnic Institute and state University , Blacksburg, November 14, VA 24061.
Wolfe P., (1969), Convergence conditions for ascent method, SIAM Rev. 11, pp.226-235.
Fletcher, R.,(1987). Practical Methods of Optimization, Vol I: Unconstrained Optimization. New York: Wiley.
Fletcher, R. and Reeves, C. (1964), Function minimization by conjugate gradients. J. Comput., 7, 149–154.
Hestenes, M.R. and Stiefel, E. L. ,(1952), Method of conjugate gradient for solving linear systems. J. Res. Natl.Bur. Stand., 49, 409–432.
Omar D. H., (2013), Numerical Methods for Unconstrained Optimization Algorithms with Chaos Theory , University of Zakho, Kurdistan Region-Iraq.
Polak,E. and Ribiere, G., (1969), Note surla convergence des methods' de directions conjugu´ ees. Rev. Fr.Imform. Rech. Op-er., 16, 35–43.
Watson L. T. and Haftka, (1988), Modern Homotopy Methods in Optimization, TR 88-51, Virginia Polytechnic Institute and state University , Blacksburg, November 14, VA 24061.
Wolfe P., (1969), Convergence conditions for ascent method, SIAM Rev. 11, pp.226-235.
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Published
2016-12-30
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Science Journal of University of Zakho
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Copyright (c) 2016 Salah G. Shareef, Dlovan H. Omar
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How to Cite
Shareef, S. G., & Omar, D. H. (2016). New Proposed Conjugate Gradient Method for Nonlinear Unconstrained Optimization. Science Journal of University of Zakho, 4(2), 248-252. https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/357
