13
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A new family of conjugate gradient methods to solve unconstrained optimization problems

, &
Pages 811-820 | Received 01 Dec 2021, Published online: 11 Aug 2022

References

  • Andrei N., (2008). An Unconstrained Optimization test function collection. Adv. Model. Optimization, 10. 147-161.
  • Al-Baali M., (1985), Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5, 121-124. doi: 10.1093/imanum/5.1.121
  • Hassan B.A., Sadiq. H. M., (2013). A Nonlinear Conjugate Gradient Method Based on a Modified Secant Condition. Iraqi Journal of Statistical Sciences. 24, 1-16.
  • Hassan B.A., Younis, M.S. Taha M.W., Ibrahim A.H., (2021), A New Type of Step Sizes for Unconstrained Optimization, 2nd International Virtual Conference on Pure Science (2IVCPS 2021), Journal of Physics: Conference Series, 1-6.
  • Hassan B.A., Muangchoo, K. Alfarag, F. Ibrahim A.H., Abubakar. A.B. (2021), An improved quasi-Newton equation on the quasi-Newton methods for unconstrained optimizations, Indonesian Journal of Electrical Engineering and Computer Science. 22(2), 389-397.
  • Hassan B.A., Sulaiman, R.M. (2021), A new class of self-scaling for quasi-Newton method based on the quadratic model, Indonesian Journal of Electrical Engineering and Computer Science, 21(3), 1830-1836. doi: 10.11591/ijeecs.v21.i3.pp1830-1836
  • Hassan B.A., E. S. Al-Rawi, (2021) A modified Newton’s method for solving functions of one variable, Ital. J. Pure Appl. Math. N. 46 577-582.
  • Hassan B.A., Kahya, M.A. (2021), A new class of quasi-Newton updating formulas for unconstrained optimization, Journal of Interdisciplinary Mathematics, 24(8), 2355-2366. https://doi.org/10.1080/09720502.2021.1961980
  • Dai, Y. H., Liao, L. Z. (2001). New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43(1), 87-101. doi: 10.1007/s002450010019
  • Dai, Y. H., Yuan, Y. (1999). A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10(1), 177-182. doi: 10.1137/S1052623497318992
  • Fletcher, R., Revees, C. M. (1964). Function minimization by conjugate gradients. Comput. J. 7(2), 149-154. doi: 10.1093/comjnl/7.2.149
  • Fletcher, R. (1987). Practical Methods of Optimization, Unconstrained Optimization. New York, NY: Wiley.
  • Hestenes, M. R., Stiefel, E. L. (1952). Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stan. 49(6), 409-436. doi: 10.6028/jres.049.044
  • Jian H., Zong-Chuan W., Qing C., (2018), An unconstrained optimization reformulation for the nash game, Journal of Interdisciplinary Mathematics. 21(5), 1303-1307. https://doi.org/10.1080/09720502.2018.1498003
  • Liu, Y., Storey, C. (1991). Efficient generalized conjugate gradient algorithms, part 1, theory. J. Optim. Theory Appl. 69(1), 129-137. doi: 10.1007/BF00940464
  • Nocedal, J., Wright, S. J. (2006). Numerical Optimization. New York, NY: Springer.
  • Polak E., Ribiere, G. (1969). Note sur la convergence de directions conjugate. Riro. Operationelle 16,: 35-43.
  • Razieh D., Narges B., Mohammad M., (2019), A new modified BFGS method for solving systems of nonlinear equations, Journal of Interdisciplinary Mathematics, 1, 75-89.
  • Sunil D., Mukesh K. G., (2022), A statistically based sentence scoring method using mathematical combination for extractive Hindi text summarization, Journal of Interdisciplinary Mathematics, 25(3), 773-790. https://doi.org/10.1080/09720502.2021.2015096
  • Yasushi N. and Hideaki I., (2011). Conjugate gradient methods using value of objective function for unconstrained. Optimization Letters, 6(5), 941-955.
  • Zoutendijk G., (1970), Nonlinear programming, computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 37-86.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.