A New Paired Spectral Gradient Method to Improve Unconstrained and Non-Linear Optimization | ||
| Kirkuk Journal of Science | ||
| Article 3, Volume 18, Issue 2, June 2023, Pages 24-31 PDF (333.74 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.32894/kujss.2022.136257.1078 | ||
| Authors | ||
| Siham I. Aziz* 1; Zeyad M. Abdullah2 | ||
| 1Department of Mathematics, College of Computers Sciences and Mathematics, University of Tikrit , Tikrit Iraq | ||
| 2Computer Department, Collage of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq. | ||
| Abstract | ||
| The conjugated spectral gradient (SCG) method is an effective method for non-constrained large-scale nonlinear optimization. In this work, a new spectral conjugate gradient method is proposed with a strong Wolfe-Powell line search (SWP). The new proposal is based on using the formula obtained by comparing the proposed algorithm with previously published conjugate gradient algorithms. Under the usual assumptions, the descent properties and overall global convergence of the proposed method are proved. The proposed method is numerically proven to be effective. | ||
| Keywords | ||
| unconstrained optimization; conjugate gradient method; sufficient descent property | ||
| References | ||
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[1] Asmaa M. Abdulrahman and Bayda G. Fathi. A modified conjugate gradient method with global convergence for unconstrianed optimization probems. Journal of Duhok University, 24(2):55–61, 2021, doi:10.26682/sjuod.2021.24.2.6. [2] Huda I. Ahmed and Ghada M. Al-Naemi. New two types of conjugate gradient algorithms for unconstrained optimization problems. Journal of Engineering Mathematics, 2(5):237–246, 2011. [3] Neculai Andrei. Conjugate gradient algorithms for molecular formation under pairwise potential minimization. In Proceedings of the Fifth Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Constanta, Romania, pages 10–13, 2006. [4] Ghada Moayid Al-Naemi and ET. Hamed. New conjugate gradient method with wolfe type line searches for nonlinear programming. Australian Journal of Basic and Applied Sciences, 7(14):622–632, 2013. [5] Liu. Jinkui, Du. Xianglin, and Wang Kairong. A mixed spectral cd-dy conjugate gradient method. Journal of Applied Mathematics, 2012, 2012, doi:10.1155/2012/569795. [6] N. Andrei. Test functions for unconstrained optimization. research institute for informatics. pages 8–10, 2004. [7] Xuesha Wu. A new spectral polak-ribi `ere-polyak conjugate gradient method. Science Asia, 41:345–349, 2015, doi: 10.2306/scienceasia1513-1874.2015.41.345. [8] Guanghui Zhou and Qin Ni. A spectral dai-yuan-type conjugate gradient method for unconstrained optimization. Mathematical Problems in Engineering, 2015:1–7, 2015, doi:10.1155/2015/839659. [9] Saman Babaie-Kafaki. A modified three–term conjugate gradient method with sufficient descent property. Applied Mathematics-A Journal of Chinese Universities, 30:263–272, 2015, doi:10.1007/s11766-015-3276-9. [10] Basim A. Hassan and Hameed M. Sadeq. The new algorithm form of the fletcher–reeves conjugate gradient algorithm. Journal of Multidisciplinary Modeling and Optimization, 1(1):41–51, 2018. [11] Yiu-ming Cheung and Jian Lou. Proximal average approximated incremental gradient descent for compositepenalty regularized empirical risk minimization. Machine Learning, 106:595–622, 2017, doi:10.1007/s10994-016-5609-1.
[12] Alaa Saad Ahmed, Hisham M. Khudhur, and Mohammed S Najmuldeen. A new parameter in three-term conjugate gradient algorithms for unconstrained optimization. Indones. J. Electr. Eng. Comput. Sci, 23(1):338–344,2021, doi:10.11591/ijeecs.v23.i1.pp338-344. [13] Mustafa Mamat, Ibrahim Mohammed Sulaiman, Malik Maulana, Zahrahtul Amani Zakaria, et al. An efficient spectral conjugate gradient parameter with descent condition for unconstrained optimization. Journal of Advanced Research in Dynamical and Control Systems, 12(2):2487–2493, 2020, doi:10.5373/JARDCS/V12I2/S20201296.
[14] Michael JD. Powell. Nonconvex minimization calculations and the conjugate gradient method. In Numerical Analysis: Proceedings of the 10th Biennial Conference held at Dundee, Scotland, June 28–July 1, 1983, pages 122–141. Springer, 1984.
[15] G. Zoutendijk. Some algorithms based on the principle of feasible directions. Elsevier, 1970, doi:10.1016/B978-0-12-597050-1.50008-7.
[16] Gaoyi Wu., Yong Li., and Gonglin Yuan. A three-term conjugate gradient algorithm with quadratic convergence for unconstrained optimization problems. Mathematical Problems in Engineering, 2018, 2018, doi:10.1155/2018/4813030.
[17] Hussein A. Wali and Khalil K. Abbo. A new formula for conjugate gradient in unconstrained optimization. AL-Rafidain Journal of Computer Sciences and Mathematics, 14(1):41–52, 2020, doi: 10.33899/CSMJ.2020.164798.
[18] Y. H. Dai and L. Z. Liao. New conjugacy conditions and related nonlinear conjugate gradient methods. Applied Mathematics and optimization, 43:87–101, 2001, doi:10.1007/s002450010019.
[19] Zhong Wan, ZhanLu Yang, and YaLin Wang. New spectral prp conjugate gradient method for unconstrained optimization. Applied Mathematics Letters, 24(1):16–22, 2011, doi:10.1016/j.aml.2010.08.002.
[20] Philip Wolfe. Convergence conditions for ascent methods. SIAM review, 11(2):226–235, 1969.
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