A new family of conjugate gradient coefficient with application

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    Conjugate gradient (CG) methods are famous for their utilization in solving unconstrained optimization problems, particularly for large scale problems and have become more intriguing such as in engineering field. In this paper, we propose a new family of CG coefficient and apply in regression analysis. The global convergence is established by using exact and inexact line search. Numerical results are presented based on the number of iterations and CPU time. The findings show that our method is more efficient in comparison to some of the previous CG methods for a given standard test problems and successfully solve the real life problem.

     

     


  • Keywords


    conjugate gradient method; conjugate gradient coefficient; global convergence; line search; regression analysis.

  • References


      [1] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, Global Convergence Properties of a New Class of Conjugate Gradient Methods for Unconstrained Optimization, Applied Math. Sci., 8 (67) (2014), 3307-3319.

      [2] A. Abashar, M. Mamat, M. Rivaie, I. Mohd, O. Omer, The Proof of Sufficient Descent Condition for a New Type of Conjugate Gradient Methods, AIP Conf. Proc., 1602 (2014), 296-303.

      [3] A. U. Moyi, L. W. June, I. Saidu, on the Application of Three-Term Conjugate Gradient Method in Regression Analysis, Int. J. Comput. Appl., (0975 8887) 102 (8) (2014).

      [4] E. Dolan, J.J. More, Benchmarking optimization software with performance profile, Math. Prog., 91 (2002) 201–213.

      [5] E. Polak, G. Ribiere, Note sur la convergence de directions conjugees, Rev. Francaise Inform. Recherche Operationelle, 3 (1969) 35–43.

      [6] G. Zoutendijk, Nonlinear programming computational methods, in: Abadie J. (Ed.) Integer and nonlinear programming, North Holland, Amsterdam, 1970.

      [7] I. Jusoh, M. Mustafa, M. Rivaie, A new edition of conjugate gradient methods for large-scale unconstrained optimization, Int. J. of Math. Anal., 8 (2014) 2277–2291.

      [8] I. S. Mohammed, M. Mamat, A. Abashar, M. Rivaie, Z. Salleh, A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization, Applied Math. Sci., 9 (54) (2015), 2671-2682.

      [9] K.E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw., 3 (1977) 305–315.

      [10] K. U. Kamfa, M. Mamat, A. Abashar, M. Rivaie, P. L. Ghazali, Z Salleh, Another Modified Conjugate Gradient Coefficient with Global Convergence Properties, Applied Math. Sci., 9 (37) (2015), 1833-1844.

      [11] M. Hamoda, A. Abashar, M. Mamat, M. Rivaie, A Comparative Study of Two New Conjugate Gradient Methods, AIP Conf. Proc., 1643 (2015), 616-621.

      [12] M. Hamoda, M. Rivaie, M. Mamat, Z. Salleh, A Conjugate Gradient Method with Inexact Line Search for Unconstrained Optimization, Applied Math. Sci., 9 (37) (2015), 1823-1832.

      [13] M. Mamat, M. Rivaie, I. Mohd, M. Fauzi, A New Conjugate Gradient Methods for Unconstrained Optimization, Int. J. Contemp. Math. Sciences, 5 (29) (2010), 1429-1437.

      [14] M.R. Hestenes, E. Steifel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952) 409–436.

      [15] M. Rivaie, A. Abashar, M. Mamat, I. Mohd, The Convergence Properties of a New Type of Conjugate Gradient Methods, Applied Math. Sci., 8 (1) (2014), 33-44.

      [16] M. Rivaie, M. Mustafa, A. Abashar, A new class of nonlinear conjugate gradient coefficient with exact and inexact line searches, Appl. Math. Comp., 268 (2015), 1152–1163.

      [17] M. Rivaie, M. Mustafa, L.W. June, I. Mohd, A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comp., 218 (2012), 11323–11332.

      [18] Rivaie, M., Mamat, M., Mohd, I., Fauzi, M.,Comparative study of conjugate gradient coefficient for unconstrained optimization (2011), Australian Journal of Basic and Applied Sciences, 5 (9), 947-951

      [19] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim., 10 (2008) 147–161.

      [20] N. Andrei, 40 conjugate gradients algorithms for unconstrained optimization, Bull. Malays. Math. Sci. Soc., 34 (2011) 319–330.

      [21] N. Hajar, M. Mamat, M. Rivaie, Z Salleh, A Combination of Polak-Ribiere and Hestenes-Steifel Coefficient in Conjugate Gradient Method for Unconstrained Optimization, Applied Math. Sci., 9 (63) (2015), 3119-3130.

      [22] N. H. M. Yussoff, M. Mamat, M. Rivaie, I. Mohd, A New Conjugate Gradient Methods for Unconstrained Optimization with Sufficient Descent, AIP Conf. Proc., 1602 (2014), 514-519.

      [23] N. Shapiee, M. R. M. Ali, M. Mamat, Z Salleh, A New Simple Conjugate Gradient Coefficient for Unconstrained Optimization, Applied Math. Sci., 9 (63) (2015), 3119-3130.

      [24] N. Shapiee, M. Rivaie, M. Mamat, I. Mohd, A New Modification of Hestenes-Stiefel with Descent Properties, AIP Conf. Proc., 1602 (2014), 520-526.

      [25] N. Shapiee, M. Rivaie, M. Mamat, A new classical conjugate gradient coefficient with exact line search, AIP Conf. Proc., 1739 (2016), 020082.

      [26] N. Zull, M. Rivaie, M. Mamat, Z Salleh, Z. Amani, Global Convergence Properties of a New Spectral Conjugate Gradient by Using Strong Wolfe Line Search, Applied Math. Sci., 9 (63) (2015), 3105-3117.

      [27] O. Omer, M. Mamat, A. Abashar, M. Rivaie, The Global Convergence Properties of a Conjugate Gradient Method, AIP Conf. Proc., 1602 (2014), 286-295.

      [28] R. B. Yunus, M. Mamat, A. Abashar, M. Rivaie, Z Salleh, Z. A. Zakaria, The Convergence Properties of a New Kind of Conjugate Gradient Methods for Unconstrained Optimization, Applied Math. Sci., 9 (38) (2015), 1845-1856.

      [29] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley and Sons, New York, 1987.

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

      [31] S. Shoid, M. Rivaie, M. Mamat, I. Mohd, Solving Unconstrained Optimization with a New Type of Conjugate Gradient Method, AIP Conf. Proc. 1602 (2014), 574-579.

      [32] Y.H. Dai, Y. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim., 10 (1999) 177–182.

      [33] Y. H. Dai and Y. Yuan, A note on the nonlinear conjugate gradient method, J. Compt. Appl. Math., 18 (2002), 575-582.

      [34] Y. H. Dai and Y. Yuan, Nonlinear conjugate gradient method, Beijing, Shanghai Scientific and Technical Publishers, (1998).

      [35] Y. Yuan and W. Sun, Theory and methods of optimization, Beijing, Science Press of China, (1999).

      [36] Y. Narushima, H. Yabe and J. A. Ford, A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim., 21 (2011), 212-230.

      [37] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Comput. Appl. Math. 69 (1992) 129–137.

      [38] Z. Z. Abidin, M. Mamat, M. Rivaie, A new steepest descent method with global convergence properties, AIP Conf. Proc., 1739 (2016), 020070.

      [39] N.H.A Ghani, M. Rivaie, M. Mamat, A Modified form of Conjugate Gradient method for Unconstrained Optimization Problems, AIP Conf. Proc., 1739 (2016), 020076.

      [40] Abidin, N.Z., Mamat, M., Dangerfield, B., Zulkepli, J.H., Baten, Md. A., Wibowo, A. Combating obesity through healthy eating behavior: A call for system dynamics optimization (2014) Plos One, 9 (12), e114135.

      [41] Mamat, M., Subiyanto, Kartono, A. Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy (2013) Applied Mathematical Sciences, 7 (5-8), 247-261.

      [42] Mamat, M., Deraman, S.K., Noor, N.M.M., Rokhayati, Y., Diet problem and nutrient requirement using Fuzzy Linear Programming Approach (2012) Asian Journal of Applied Sciences, 5 (1), 52-59.

      [43] Mamat, M., Rokhayati, Y., Noor, N.M.M., Mohd, I., Optimizing human diet problem with fuzzy price using fuzzy linear programming approach (2011) Pakistan Journal of Nutrition, 10 (6), 594-559.


 

View

Download

Article ID: 20962
 
DOI: 10.14419/ijet.v7i3.28.20962




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.