A New Conjugate Gradient Coefficient for Unconstrained Optimization Based On Dai-Liao

  • Alaa L. Ibrahim Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq (alaa.ibrahim@uod.ac)
  • Muhammad A. Sadiq College of Administration and Economics, Cihan University Duhok, Kurdistan Region-Iraq (muhammad.math@uod.ac)
  • Salah G. Shareef Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq (salah.shareef@uoz.edu.krd)
Keywords: conjugate gradient, unconstrained optimization, Barzilai and Borwein step size, descent and sufficient descent conditions

Abstract

This paper, proposes a new conjugate gradient method for unconstrained optimization based on Dai-Liao (DL) formula; descent condition and sufficient descent condition for our method are provided. The numerical results and comparison show that the proposed algorithm is potentially efficient when we compare with (PR) depending on number of iterations (NOI) and the number of functions evaluation (NOF).

References

Barzilai, J. and Borwein, J.M. (1988), Tow point step size gradient methods, IMA J. Numer. Anal., 8, 141-148.
Dai, Y. H. and Liao, L.Z., (2001), New conjugacy conditions and related nonlinear conjugate gradient methods, Application Mathematical Optimization, 43, 87-101.
Dai, Y. H. and Yuan, Y., (1996), Convergence properties of the Fletcher-Reeves method, IMAJ. Numer. Anal., 2, 155-164.
Fletcher, R. and Reeves, C.M., (1964), Function minimization by conjugate gradients, The Computer Journal. 7, 149-154.
Fletcher, R., (1987), Practical methods of optimization unconstrained optimization, John Wiley & Sons, New York, NY, USA.
Hager,W. W. and Zhang, H., (2006),A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2, 35-58.
Hestenes, M. R. and Stiefel, E., (1952), Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards. 49, 409-436.
Liu, Y. and Storey, C., (1991), Efficient generalized conjugate gradient algorithms, part 1: Theory, Journal of Optimization Theory and Applications, 69, 129-137.
Polak, E. and Ribiere, G., (1969), Note surla convergence des méthodes de directions conjuguées., 3(16), 35-43.
Polyak, B. T., (1969), The conjugate gradient method in extreme problems, USSR Comp. Math. and Math. Phys., 94-112.
Wolfe, P. (1969), Convergence conditions for ascent methods, SIAM. Rev. 11, 226-235.
Published
2019-03-30
How to Cite
Ibrahim, A., Sadiq, M., & Shareef, S. (2019). A New Conjugate Gradient Coefficient for Unconstrained Optimization Based On Dai-Liao. Science Journal of University of Zakho, 7(1), 34-36. https://doi.org/10.25271/sjuoz.2019.7.1.525
Section
Science Journal of University of Zakho