Conjugate gradient method for solving unconstrained optimization problems: A new investigation and application
*Huda Y. NajmCorresponding authorhuda.najm@uod.acDepartment of MathematicsCollege of ScienceUniversity of DuhokKurdistan Region, IraqView full profile → , Huda I. Ahmedhudaea72@gmail.comDepartment of Operation Researches and Intelligent TechniquesCollege of Computers Sciences and MathematicsUniversity of MosulMosul, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jan 2022
- Accepted:
- 01 Mar 2022
- Published Online:
- 15 Jul 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1465
- Pages:
- 601–611
Abstract
Keywords
Subject Classifications
References
[1] F. N. Jardow and G. M. Al-Naemi, “A new hybrid conjugate gradient algorithm as a convex combination of MMWU and RMIL nonlinear problems,” Journal of Interdisciplinary Mathematics, Vol. 24, No. 3, pp. 637–655 (2021), doi: 10.1080/09720502.2020.1815346.
[2] H. H. Dwail, M. M. Mahdi, and M. A. K. Shiker, “CG method with modifying β k for solving unconstrained optimization problems,” Journal of Interdisciplinary Mathematics (2022), doi: 10.1080/09720502.2022.2040854.
[3] M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Journal of Research of the National Bureau of Standards, Vol. 49, No. 6. p. 409 (1952), doi: 10.6028/jres.049.044.
[4] R. Fletcher and C.M. Reeves, “Function minimization by conjugate gradients,” Comput. J, pp. 149–154 (1964).
[5] Polak & Ribiere, “Note sur la convergence de méthodes de directions conjuguées,” Rech. Opérationnelle. Série Rouge, Vol. 3, No. 16, pp. 35–43 (1969).
[6] B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Comput. Math. Math. Phys., Vol. 9, No. 4, pp. 94–112 (1969), doi: 10.1016/0041-5553(69)90035-4.
[7] 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), doi: 10.1137/S1052623497318992.
[8] Y. H. Dai and L. Z. Liao, “New conjugacy conditions and related nonlinear conjugate gradient methods,” Appl. Math. Optim., Vol. 43, No. 1, pp. 87–101 (2001), doi: 10.1007/s002450010019.
[9] A. Perry, “Technical Note—A Modified Conjugate Gradient Algorithm,” Oper. Res., Vol. 26, No. 6, pp. 1073–1078 (1978), doi: 10.1287/opre.26.6.1073.
[10] W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an efficient line search,” SIAM J. Optim., Vol. 16, No. 1, pp. 170–192 (2006), doi: 10.1137/030601880.
[11] N. Andrei, “A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues,” Numer. Algorithms, Vol. 77, No. 4, pp. 1273–1282 (2018), doi: 10.1007/s11075-017-0362-5.
[12] S. Yao, L. Ning, H. Tu, and J. Xu, “A one-parameter class of three-term conjugate gradient methods with an adaptive parameter choice,” Optim. Methods Softw., Vol. 35, No. 6, pp. 1051–1064 (2020), doi: 10.1080/10556788.2018.1510926.
[13] M. A. H. Bin Ibrahim, M. Mamat, and L. W. June, “BFGS method: A new search direction,” Sains Malaysiana, Vol. 43, No. 10, pp. 1591–1597 (2014).
[14] J. Barzilai, “Two-point step size gradient methods.pdf,” no. November, pp. 141–148 (2017).
[15] A. Y. Al-Bayati, “A new family of self-scaling variable metric algorithms for unconstrained optimization,” J. Educ. Sci. Mosul Univ., Vol. 12, pp. 25-54.
[16] 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), doi: 10.1137/0802003.
[17] A. UsmanMoyi, W. June Leong, and I. Saidu, “On the Application of Three-Term Conjugate Gradient Method in Regression Analysis,” Int. J. Comput. Appl., Vol. 102, No. 8, pp. 1–4 (2014).
[18] G. Yuan and Z. Wei, “New line search methods for unconstrained optimization,” J. Korean Stat. Soc., Vol. 38, No. 1, pp. 29–39 (2009), doi: 10.1016/j.jkss.2008.05.004.
[19] W. C. (COVID-19) Dashboard, “https://covid19.who.int/table,” Iraq, 2021. https://covid19.who.int/table.
