A modified hybrid conjugate gradient method for solving unconstrained non-linear optimization problems has been developed


Abstract views: 144 / PDF downloads: 77

Authors

  • Chenna Nasreddine Souk Ahras University

DOI:

https://doi.org/10.59287/icpis.884

Keywords:

Optimization, Algorithm, Descent Direction, Line Search, Conjugate Gradient

Abstract

This paper presents a new hybrid conjugate gradient method, combining the Conjugate Descent (CD) and Al-Bayati & Al-Assady (BA) methods, for solving unconstrained optimization problems. We provide a convergence analysis of the proposed method and demonstrate its effectiveness through numerical examples.

Author Biography

Chenna Nasreddine, Souk Ahras University

Laboratory Mathematics and Informatics, Algeria

References

N. Andrei, A hybrid conjugate gradient algorithm for unconstrained optimization as a convex combination of Hestenes-Stiefel and Dai-Yuan, Studies in Informatics and Control, 17, 1 (2008) 55-70.

Y. Liu, C. Storey, E cient generalized conjugate gradient algorithms, Part 1: Theory, JOTA, 69 (1991) 129137.

Al-Bayati, A.Y. and Al-Assady, N.H (1986), Conjugate Gradient Method, Technical Report, no.(1/86), School of Computer Studies, Leeds University. U.K R.

Fletcher, Practical Methods of Optimization, vol. 1: Unconstrained Optimization, JohnWiley and Sons, New York, 1987.

N. Chenna, Comments on ”New Hybrid Conjugate Gradient Method as a Convex Combination of FR and PRP Methods”, Filomat 33:14 (2019), 4573–4574.

N. Chenna, A new hybrid conjugate gradient method of unconstrained optimization methods, Asian-European Journal of Mathematics Vol. 15, No. 4 (2022) 2250070 (11 pages).

P.Wolfe, Convergence conditions for ascent methods, SIAM Review, 11 (1969) 226-235.

B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Math. Phys., 9 (1969) 94-112.

G. Zoutendijk, Nonlinear programming computational methods, in: J.Abadie (Ed.), Integer and Nonlinear Programming, North-Holland, 1970, pp. 37-86.

J.K. Liu, S.J. Li, New hybrid conjugate gradient method for unconstrained optimization, Applied Mathematics and Computation, 245 (2014) 36-43.

Downloads

Published

2023-06-20

How to Cite

Nasreddine, C. (2023). A modified hybrid conjugate gradient method for solving unconstrained non-linear optimization problems has been developed. International Conference on Pioneer and Innovative Studies, 1, 524–526. https://doi.org/10.59287/icpis.884

Conference Proceedings Volume

Section

Conference Papers