The application of new conjugate gradient methods in estimating data

  • Authors

    • Syazni Shoid
    • Norrlaili Shapiee
    • Norhaslinda Zull
    • Nur Hamizah Abdul Ghani
    • Nur Syarafina Mohamed
    • Mohd Rivaie
    • Mustafa Mamat
    2018-04-06
    https://doi.org/10.14419/ijet.v7i2.14.11147
  • Conjugate Gradient Coefficient, Inexact Line Search, Least Squares, Regression, Strong Wolfe Powell

  • Many researchers are intended to improve the conjugate gradient (CG) methods as well as their applications in real life. Besides, CG become more interesting and useful in many disciplines and has important role for solving large-scale optimization problems. In this paper, three types of new CG coefficients are presented with application in estimating data. Numerical experiments show that the proposed methods have succeeded in solving problems under strong Wolfe Powell line search conditions.

     

  • References

    1. [1] Fletcher R & Reeves C, Function minimization by conjugate gradients (1964), Comput J 7, 149-154.

      [2] Polak E & Ribiere G, Note sur la convergence de directions conjugees (1969), Rev.Francaise Informat Recherche Operationelle,3E Annee 16, 35-43.

      [3] Hestenes MR & Steifel E, Method of conjugate gradient for solving linear equations (1952), J,Res.Nat.Bur.Stand 49, 409-436.

      [4] Rivaie M, Mamat M, Leong WJ & Ismail M, A new conjugate gradient coefficient for large scale nonlinear unconstrained optimization (2012), Int. Journal of Math. Analysis 6, 23 1131-1146.

      [5] Shoid S, Rivaie M & Mamat M, A modification of classical conjugate gradient method using strong Wolfe line search (2016), AIP Conf. Proc., 1739, 020071, doi: 10.1063/1.4952562.

      [6] Shapiee N, Rivaie M & Mamat M, A new classical conjugate gradient coefficient with exact line search (2016), AIP Conf. Proc. 1739,020082, doi: 10.1063/1.4952562.

      [7] Rivaie M, Abashar A, Mamat M & Mohd I, The conjugence properties of a new type of conjugate gradient methods (2014), App. Math. Science 8, no. 1, 33-44.

      [8] Ghani NHA, Rivaie M & Mamat M, A modified form of conjugate gradient method for unconstrained optimization problems (2016), AIP Conf. Proc. 1739, 020076, doi: 10. 1063/1.4952556.

      [9] Hajar N, Mamat M, Rivaie M & Jusoh I, A new type of desent conjugate gradient method with exact line search (2016), AIP Conf. Proc. 1739, 020089, doi: 10. 1063/1.4952569.

      [10] Khadijah W, Rivaie M, Mamat M & Jusoh I, A spectral KRMI conjugate gradient method under the strong-Wolfe line search (2016), AIP Conf. Proc. 1739, 020072, doi: 10. 1063/1.4952552.

      [11] Zoutendjik G, Nonlinear programming computational methods (1970), in: J. Abadie (Ed.), Interger and Nonlinear Programming, North-Holland, Amsterdan, pp.37-86.

      [12] Al-Baali M, Descent property and global convergence of Fletcher-Reeves method with inexact line search (1985), IMA. J. Numer. Anal 5, 121-124.

      [13] Wolfe P, Convergence conditions for ascent method. II: some corrections (1971), SIAM Rev 13(2), 185-188.

      [14] Traffic Statistics Branch, Bukit Aman PDRM, RTD Corporate Division, MIROS Headquarters, Road death index 2004-2014,available online: http://www.jkjr.gov.my/ms/maklumat_keselamatan/ststik-kmlgn-jln-rya/1858-indeks-kematian-jalan-raya-2004-2014.html), 24 jun 2015.

  • Downloads

  • How to Cite

    Shoid, S., Shapiee, N., Zull, N., Hamizah Abdul Ghani, N., Syarafina Mohamed, N., Rivaie, M., & Mamat, M. (2018). The application of new conjugate gradient methods in estimating data. International Journal of Engineering & Technology, 7(2.14), 25-27. https://doi.org/10.14419/ijet.v7i2.14.11147