Two Versions of the Spectral Nonlinear Conjugate Gradient Method

Authors

  • Basim A. Hassan Department of Mathematics, College of Computers Sciences and Mathematics, University of Mosul
  • Haneen A. Alashoor Department of Mathematics, College of Computers Sciences and Mathematics, University of Mosul

DOI:

https://doi.org/10.23851/mjs.v29i1.577

Keywords:

Conjugate gradient, Spectral conjugate gradient, Descent condition, Global convergence, Numerical results.

Abstract

The nonlinear conjugate gradient method is widely used to solve unconstrained optimization problems. In this paper the development of different versions of nonlinear conjugate gradient methods with global convergence properties proved. Numerical results indicated that the proposed method is very efficient.

References

Andrie N., "An Unconstrained Optimization Test functions collection," Advanced Modeling and optimization. 10, pp.147-161, 2008.

Al-Baali, "Descent property and global convergence of the Fletcher Reeves method with inexact line search," IMA J. Numer. Anal. 5 pp. 121–124, 1985. DOI: https://doi.org/10.1093/imanum/5.1.121

Birigin, F. G. and Martinez, J. M., "A Spectral Conjugate Gradient Method for Unconstrained Optimization," Applied Mathematics and Optimization, 43, 117-128. 2001. DOI: https://doi.org/10.1007/s00245-001-0003-0

Basim A. H. and Haneen A. A., "New Nonlinear Conjugate Gradient Formulas for Solving Unconstrained Optimization Problems," Al-Mustansiriyah Journal of Science, 3, pp. 82-88. 2016.

Basim A. H. and Haneen A. A., "A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix ," 2015.

Dolan E. and More J.,"Benchmarking optimization software with performance profiles ," Math. Programming 91, pp. 201-213, 2002. DOI: https://doi.org/10.1007/s101070100263

Fletcher, R. and Reeves C."Function minimization by conjugate gradients ' Computer ", J, 7, pp. 149-154, 1964. DOI: https://doi.org/10.1093/comjnl/7.2.149

Hager W. W. and Zhang. H. "A surrevy of nonlinear conjugate gradient methods "Paaific Journal of optimization. 2006.

Zhang, L.W. Zhou, D. Li,"Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search," Numer. Math. 104, PP. 561–572, 2006. DOI: https://doi.org/10.1007/s00211-006-0028-z

Zoutendijk, G.,"Nonlinear programming, computational methods. In: Abadie, J. (eds.) Integerand Nonlinear Programming, " North-Holland, Amsterdam .pp. 37–86, 1970.

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Published

2018-10-31

How to Cite

[1]
B. A. Hassan and H. A. Alashoor, “Two Versions of the Spectral Nonlinear Conjugate Gradient Method”, MJS, vol. 29, no. 1, pp. 133–137, Oct. 2018.

Issue

Section

Mathematics