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Parameterized Three-Term Conjugate Gradient Method

Year 2020, Volume: 3 Issue: 1, 1 - 11, 17.09.2020

Abstract

In this paper a new parameterized three-term conjugate gradient algorithm is suggested, the descent property and global convergence are proved for the new suggested method. Numerical experiments are employed to demonstrate the efficiency of the algorithm for solving large scale benchmark test problems, particularly in comparison with the existent state of the art algorithms available in the literature.

References

  • [1] M. Al-Baali, Descent property and global convergence of the Fletcher Reeves method with inexact line search, IMA J. Numer. Anal., 5(1) 1985, 121-124.
  • [2] N. Andrei, New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization . In: Floudas C., Pardalos P. (eds) Encyclopedia of Optimization, Springer, Boston, 2008, 2560-2571.
  • [3] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim, 10(1) 2008, 147-161.
  • [4] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1) 1993, 123-160.
  • [5] Y. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optimiz., 10(1) 1999, 177-182.
  • [6] L. C.W. Dixon, Nonlinear optimization: A survey of the state of the art, Hatfield Polytechnic. Numerical Optimization Centre, 1973.
  • [7] D. Dolan, J. Mor´e, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.
  • [8] K. Edwin, H. Stanilow, An introduction to optimization, Second Edition, Wiley and Sons, 2001.
  • [9] R. Fletcher, C. M. Reeves, Function minimization by Conjugate gradients, Comput. J., 7(2) 1964, 149-154.
  • [10] W. Hager, H. Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2(1), 2006, 35-58.
  • [11] M. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952.
  • [12] K. K. Abbo, L. A. Abdulwahid, Generalized Dai-Yuan non-linear conjugate gradient method for unconstrained optimization, Int. J. Sci. Math. Educ., 8(6) 2017, 17993-17999.
  • [13] X. Li, X. Zhao, A hybrid conjugate gradient method for optimization problems, Nat. Sci., 3(1) 2011, 85.
  • [14] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optimiz. Theory App., 69(1) 1991, 129-137.
  • [15] J. Nocedal, J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer Verlag, New York, 2006.
  • [16] E. Polak and G. Ribiere, Note sur la convergence de m´ethodes de directions conjugu´ees, Rev. Fr. Inform. Rech. O., 3(16) 1969, 35-43.
  • [17] S. S. Djordjevi, New hybrid conjugate gradient method as a convex combination of FR and PRP Methods. Filomat, 30(11) 2016, 3083-3100.
  • [18] P. Wolfe, Convergence conditions for ascent methods, SIAM Rev., 11(2) 1969, 226-235.
Year 2020, Volume: 3 Issue: 1, 1 - 11, 17.09.2020

Abstract

References

  • [1] M. Al-Baali, Descent property and global convergence of the Fletcher Reeves method with inexact line search, IMA J. Numer. Anal., 5(1) 1985, 121-124.
  • [2] N. Andrei, New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization . In: Floudas C., Pardalos P. (eds) Encyclopedia of Optimization, Springer, Boston, 2008, 2560-2571.
  • [3] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim, 10(1) 2008, 147-161.
  • [4] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1) 1993, 123-160.
  • [5] Y. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optimiz., 10(1) 1999, 177-182.
  • [6] L. C.W. Dixon, Nonlinear optimization: A survey of the state of the art, Hatfield Polytechnic. Numerical Optimization Centre, 1973.
  • [7] D. Dolan, J. Mor´e, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.
  • [8] K. Edwin, H. Stanilow, An introduction to optimization, Second Edition, Wiley and Sons, 2001.
  • [9] R. Fletcher, C. M. Reeves, Function minimization by Conjugate gradients, Comput. J., 7(2) 1964, 149-154.
  • [10] W. Hager, H. Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2(1), 2006, 35-58.
  • [11] M. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952.
  • [12] K. K. Abbo, L. A. Abdulwahid, Generalized Dai-Yuan non-linear conjugate gradient method for unconstrained optimization, Int. J. Sci. Math. Educ., 8(6) 2017, 17993-17999.
  • [13] X. Li, X. Zhao, A hybrid conjugate gradient method for optimization problems, Nat. Sci., 3(1) 2011, 85.
  • [14] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optimiz. Theory App., 69(1) 1991, 129-137.
  • [15] J. Nocedal, J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer Verlag, New York, 2006.
  • [16] E. Polak and G. Ribiere, Note sur la convergence de m´ethodes de directions conjugu´ees, Rev. Fr. Inform. Rech. O., 3(16) 1969, 35-43.
  • [17] S. S. Djordjevi, New hybrid conjugate gradient method as a convex combination of FR and PRP Methods. Filomat, 30(11) 2016, 3083-3100.
  • [18] P. Wolfe, Convergence conditions for ascent methods, SIAM Rev., 11(2) 1969, 226-235.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Khalil Abbo

Nehal H. Hameed

Publication Date September 17, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Abbo, K., & Hameed, N. H. (2020). Parameterized Three-Term Conjugate Gradient Method. Journal of Multidisciplinary Modeling and Optimization, 3(1), 1-11.
AMA Abbo K, Hameed NH. Parameterized Three-Term Conjugate Gradient Method. jmmo. September 2020;3(1):1-11.
Chicago Abbo, Khalil, and Nehal H. Hameed. “Parameterized Three-Term Conjugate Gradient Method”. Journal of Multidisciplinary Modeling and Optimization 3, no. 1 (September 2020): 1-11.
EndNote Abbo K, Hameed NH (September 1, 2020) Parameterized Three-Term Conjugate Gradient Method. Journal of Multidisciplinary Modeling and Optimization 3 1 1–11.
IEEE K. Abbo and N. H. Hameed, “Parameterized Three-Term Conjugate Gradient Method”, jmmo, vol. 3, no. 1, pp. 1–11, 2020.
ISNAD Abbo, Khalil - Hameed, Nehal H. “Parameterized Three-Term Conjugate Gradient Method”. Journal of Multidisciplinary Modeling and Optimization 3/1 (September 2020), 1-11.
JAMA Abbo K, Hameed NH. Parameterized Three-Term Conjugate Gradient Method. jmmo. 2020;3:1–11.
MLA Abbo, Khalil and Nehal H. Hameed. “Parameterized Three-Term Conjugate Gradient Method”. Journal of Multidisciplinary Modeling and Optimization, vol. 3, no. 1, 2020, pp. 1-11.
Vancouver Abbo K, Hameed NH. Parameterized Three-Term Conjugate Gradient Method. jmmo. 2020;3(1):1-11.