A New Scaled Three-Term Conjugate Gradient Algorithms For Unconstrained Optimization

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Zeyad M. Abdullah
Songul A. Asker

Abstract

Since optimization problems are getting more complicated, new ways to solve them must be thought of, or existing methods must be improved. In this research, we expand the different parameters of the three-term conjugate gradient method to work out unconstrained optimization problems. Our new CG approach meets the conditions of sufficient descent, and global convergence. In addition, we describe some numerical results that imply comparisons to relevant methodologies in the existing research literature.

Article Details

How to Cite
Abdullah, Z. M., & Asker, S. A. (2023). A New Scaled Three-Term Conjugate Gradient Algorithms For Unconstrained Optimization. Tikrit Journal of Pure Science, 28(4), 103–110. https://doi.org/10.25130/tjps.v28i4.1534
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Articles

References

[1] J. C. Gilbert and J. Nocedal, “Global convergence properties of conjugate gradient methods for optimization,” SIAM J. Optim., vol. 2, no. 1, pp. 21–42, 1992.

[2] A. Y. Al-bayati and R. S. Muhammad, “New Scaled Sufficient Descent Conjugate Gradient Algorithm for Solving Unconstraint Optimization Problems 1,” 2010.

[3] M. S. Jameel, Z. M. Abdullah, F. A. Fawzi, and B. A. Hassan, “A New Shifted Conjugate Gradient Method” Based” on Shifted Quasi-Newton Condition,” in Journal of Physics: Conference Series, 2021, vol. 1818, no. 1, p. 12105.

[4] L. Zhang and W. Zhou, “Two descent hybrid conjugate gradient methods for optimization,” J. Comput. Appl. Math., vol. 216, no. 1, pp. 251–264, 2008.

[5] M. J. D. Powell, “Some global convergence properties of a variable metric algorithm for minimization without exact line searches,” in Nonlinear programming, SIAM-AMS proceedings, 1976, vol. 9.

[6] L. Zhang, W. Zhou, and D.-H. Li, “A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence,” IMA J. Numer. Anal., vol. 26, no. 4, pp. 629–640, 2006.

[7] O. A. ARIK, “Dissatisfaction levels of earliness and tardiness durations by relaxing common due date on single machine scheduling problems,” J. Multidiscip. Model. Optim., vol. 2, no. 1, pp. 1–15, 2019.

[8] A. Y. Al-Bayati and H. N. Al-Khayat, “A global convergent spectral conjugate gradient method,” Aust. J. Basic Appl. Sci., vol. 7, no. 7, pp. 302–309, 2013.

[9] Y.-H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM J. Optim., vol. 10, no. 1, pp. 177–182, 1999.

[10] N. Andrei, “An unconstrained optimization test functions collection,” Adv. Model. Optim, vol. 10, no. 1, pp. 147–161, 2008.