New Proposed Conjugate Gradient Method for Nonlinear Unconstrained Optimization

Authors

  • Salah G. Shareef University of Zakho
  • Dlovan H. Omar University of Zakho

Keywords:

Unconstrained Optimization, Conjugate Gradient Method, Homotopy Theory

Abstract

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.

Author Biographies

Salah G. Shareef, University of Zakho

Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region – Iraq.

Dlovan H. Omar, University of Zakho

Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region – Iraq.

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.

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Published

2016-12-30

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. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/357

Issue

Vol. 4 No. 2 (2016): December, 2016

Section

Science Journal of University of Zakho

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