Explaining new parameters conjugate analysis based on the quadratic model

Hassan, Basim A.; Saad, Abdulameer A.

doi:10.47974/JIM-1620

Open Access Research Article

Explaining new parameters conjugate analysis based on the quadratic model

^*Basim A. HassanCorresponding authorbasimah@uomosul.edu.iqDepartment of MathematicsCollege of Computer Science and MathematicsUniversity of MosulMosul, Iraq0000-0003-3510-9818View full profile → , Abdulameer A. Saadabdulameer2023@gmail.comDepartment of MathematicsCollege of Computer Science and MathematicsUniversity of MosulMosul, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1219–1229Vol. 26Issue 6September 2023DOI: 10.47974/JIM-1620XML

Published Online:: 08 Sep 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1620
Pages:: 1219–1229

Abstract

The coefficient conjugate is often the subject of conjugate gradient techniques. In this work, we use the quadratic function to unconstrained optimization problems and construct an unique coefficient conjugate gradient method. Based on a novel coefficient conjugate, we provided a search direction and fascinating conjugate gradient approach. We demonstrate that, given the appropriate circumstances, the proposed technique is universally convergent. Our numerical findings show that this method is effective for unconstrained optimization problems.

Keywords

Optimization Conjugate gradient methods Globally convergent Numerical results

Subject Classifications

90C3065K0549M37

Acknowledgements

FRH-P928H80

References

[1] Z. Dai, F. Wen, Some improved sparse and stable portfolio optimization problems, Finance Research Letters, 27, 46-52 (2018), http://doi:10.1016/j.frl.2018.02.026.
[2] H.N. Jabbar, B.A. Hassan, Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization, Indonesian Journal of Electrical Engineering and Computer Science, 22(3), 1643 (2021), http://doi:10.11591/ijeecs.v22.i3.1643-1649.
[3] S. Wright, J. Nocedal, others, Numerical optimization, Springer Science, 35(1), 67-68, 7 (1999), http:// doi:10.1007/978-0-387-40065-5.
[4] Y.H. Dai, L. Z Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Al Math Optim, 43(1), 87-101 (2001), http://doi:10.1007/s002450010019.
[5] R. Fletcher, C. M. Reeves, Function minimization by conjugate gradients, Comput J, 7(2), 149-154 (1964), http://doi:10.1093/comjnl/7.2.149.
[6] Y.-H. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM Journal on Optimization, 10(1), 177-182 (1999), http://doi:10.1137/S1052623497318992.
[7] R. Fletcher, Practical methods of optimization. John Wiley & Sons (2013).
[8] M. R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand. (1934)., 49(6), 409-501 (1952), http://doi:10.6028/jres.049.044.
[9] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J Optim Theory Appl, 69(1), 129-137 (1991), http://doi: org/10.1007/BF00940464.
[10] E. Polak, G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Rev. française d’informatique Rech. opérationnelle. Série rouge, 3(16), 35-43 (1969), http://doi:10.1051/m2an/196903R100351.
[11] Y.-H. Dai, Y. Yuan, Nonlinear conjugate gradient methods, Shanghai Science and Technology Publisher, Shanghai, 2000.
[12] L. Nazareth, A relationship between the BFGS and conjugate gradient algorithms and its implications for new algorithms, SIAM J Numer Anal, 16(5), 794-800 (1979), http://doi:10.1137/0716059.
[13] B.A. Hassan, M. S. Younis, M. W. Taha, A. H. Ibrahim, A New Type of Step Sizes for Unconstrained Optimization, in Journal of Physics: Conference Series, 2021, 1999(1), 12099. http://doi:10.1088/1742-6596/1999/1/012099.
[14] B.A. Hassan, K. Muangchoo, F. Alfarag, A.H. Ibrahim, A.B. Abubakar, 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 (2020), http://doi:10.11591/ijeecs. v22.i2.389-397.
[15] B.A. Hassan, Z. M. Abdullah, H. N. Jabbar, A descent extension of the Dai-Yuan conjugate gradient technique, Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 661 (2019), http:// doi:10.11591/ijeecs. v16.i2.661-668.
[16] B.A. Hassan, H. O. Dahawi, A. S. Younus, A new kind of parameter conjugate gradient for unconstrained optimization, Indonesian Journal of Electrical Engineering and Computer Science, 17(1), 404 (2020), http:// doi:10.11591/ijeecs.v17.i1.404-411.
[17] Y. Dai, J. Han, G. Liu, D. Sun, H. Yin, Y. Yuan, Convergence properties of nonlinear conjugate gradient methods, SIAM Journal on Optimization, 10(2), 345-358 (2000), http://doi:10.1137/S1052623494268443.
[18] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim, 10(1), 147-161 (2008).
[19] W. Gao, M. R. Farahani, The hyper-Zagreb index for an infinite family of nanostar dendrimer, Journal of Discrete Mathematical Sciences and Cryptography. 20(2), 515-523 (2017), http://doi:10.1080/09720529.2016.1220088.
[20] W. Gao, L. Shi, M.R. Farahani, Szeged Related Indices of TUAC6[p,q], Journal of Discrete Mathematical Sciences and Cryptography. 20(1), 553-563, 2017, http://doi:10.1080/09720529.2016.1228312.
[21] W. Gao and M. R. Farahani, The Zagreb topological indices for a type of Benzenoid systems jagged-rectangle, Journal of Interdisciplinary Mathematics, 20(5), 1341-1348 (2017), http://doi:10.1080/09720502.2016.1232037.
[22] W. Sajjad, M.S. Sardar, M. Cancan, S. Ediz, A. Q. Baig, On modified eccentric connectivity index of nanotube, Journal of Information and Optimization Sciences, 41(4), 959-972, (2020), http://doi:10.1080/02522667.2020.1745380.
[23] S. Ediz, İ. Çiftçi, M.Cancan, M.R.Farahani, On k-total distance degrees and k-total Wiener polarity index. Journal of Information and Optimization Sciences. 42(7), 1469-1477 (2021). https://doi.org/10.1080/02522667.2021.1896652.
[24] F. Afzal, Shah Rukh, D. Afzal, M.R.Farahani, M.Cancan, S. Ediz. A study of non-commutative Von-Neumann regular rings. Journal of Information and Optimization Sciences. 42(7), 1425-1436 (2021). https://doi.org/10.1080/02522667.2021.1896650.
[25] M.S. Sardar, M. Alaeiyan, M.R.Farahani, M.Cancan, S. Ediz. Resistance distance in some classes of rooted product graphs obtained by Laplacian generalized inverse method. Journal of Information and Optimization Sciences 42(7), 1447-1467 (2021). https://doi.org/10.1080/02522667.2021.1899210.
[26] M. Nadeem, S. Ahmad, M.K. Siddiqui, M.A. Ali, M.R.Farahani, A.J.M. Khalaf. On some applications related with algebraic structures through different well known graphs. Journal of Discrete Mathematical Sciences and Cryptography. 24(2), 451-471 (2021). https://doi.org/10.1080/09720529.2021.1885806.
[27] A. Alsinai, H.M.U. Rehman, Y. Manzoor, M. Cancan, Z. Taş, M.R. Farahani, Sharp upper bounds on forgotten and SK indices of cactus graph, Journal of Discrete Mathematical Sciences and Cryptography, 1-22 (2022). https://doi.org/10.1080/09720529.2022.2027605.

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