Research Article

New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods

Volume: 1 Number: 2 January 21, 2019
  • Khalil Abbo *
  • Nehal Hameed
EN

New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods

Abstract

In this paper we consider a new hybrid conjugate gradient algorithm, which is convex combination of the Liu-Story algorithm and Dixon algorithm, the descent property and global convergence are proved for the new suggested method. Numerical comparisons show that the present method often behaves better than Liu-Storey and Dixon methods. 

Keywords

References

  1. [1] N. Andrei , New hybrid conjugate gradient algorithms for unconstrained optimization, Enc. Mat. Sci., 2009 2560-2571.[2] N. Andrei, An unconstrained optimization test function collection, Adv. Model. Optim., 10(1) 2008, 147-161.[3] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1), 1993, 123–160 [4] Y. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global con-vergence property, SIAM J. Optimiz., 10(1) 1999, 177-182.[5 L. C. W. Dixon, Nonlinear optimisation: A survey of the state of the art, Hatfield Polytech-nic. Numerical Optimisation Centre (1973). [6] D. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.[7] E. K. Chong and S. H. Zak, An introduction to optimization, John Wiley & Sons 2013. [8] R. Fletcher and C. M. Reeves, Function minimization by Conjugate gradients, comput. J., 7(2) 1964, 149-154.[9] W. Hager and H. Zhang , A survey of nonlinear conjugate gradient methods, Pac. J. Op-tim., 2(1) 2006, 35-58.[10] M. Hestenes and E. Stiefel, Methods of conjugate Gradients For solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952. [11] K. K. Abbo and L. A. Abdulwahid, Generalized Dai-Yuan non-linear conjugate gradi-ent method for unconstrained optimization, Int. J. Sci. Math. Educ., 8(6) 2017, 17993-17999. [12] X. Li and X. Zhao, A hybrid conjugate gradient method for optimization problems, Nat. Sci., 3(1) 2011, 85. [13] Y. Liu and C. Story, Efficient generalized conjugate gradient algorithms, part l : Theory, J. Optimiz. Theory App., 69(1) 1991, 129-137. [14] J. Nocedal and J. Wright, Numerical Optimization, Springer Series in Operations Re-search, Springer Verlag, New York, 2006. [15] E. Polak and G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Rev. Fr. Inform. Rech. O., 3(16) 1969, 35-43.[16] S. S. Djordjević, New hybrid conjugate gradient method as a convex combination of FR and PRP Methods. Filomat, 30(11) 2016, 3083-3100. [17] P. Wolfe, Convergence conditions for ascent methods, SIAM rev., 11(2) 1969, 226-235.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Khalil Abbo * This is me
Iraq

Nehal Hameed This is me
Iraq

Publication Date

January 21, 2019

Submission Date

October 31, 2018

Acceptance Date

January 22, 2019

Published in Issue

Year 2018 Volume: 1 Number: 2

APA
Abbo, K., & Hameed, N. (2019). New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. Journal of Multidisciplinary Modeling and Optimization, 1(2), 91-99. https://izlik.org/JA37AX63CC
AMA
1.Abbo K, Hameed N. New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. jmmo. 2019;1(2):91-99. https://izlik.org/JA37AX63CC
Chicago
Abbo, Khalil, and Nehal Hameed. 2019. “New Hybrid Conjugate Gradient Method As a Convex Combination of Liu-Storey and Dixon Methods”. Journal of Multidisciplinary Modeling and Optimization 1 (2): 91-99. https://izlik.org/JA37AX63CC.
EndNote
Abbo K, Hameed N (January 1, 2019) New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. Journal of Multidisciplinary Modeling and Optimization 1 2 91–99.
IEEE
[1]K. Abbo and N. Hameed, “New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods”, jmmo, vol. 1, no. 2, pp. 91–99, Jan. 2019, [Online]. Available: https://izlik.org/JA37AX63CC
ISNAD
Abbo, Khalil - Hameed, Nehal. “New Hybrid Conjugate Gradient Method As a Convex Combination of Liu-Storey and Dixon Methods”. Journal of Multidisciplinary Modeling and Optimization 1/2 (January 1, 2019): 91-99. https://izlik.org/JA37AX63CC.
JAMA
1.Abbo K, Hameed N. New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. jmmo. 2019;1:91–99.
MLA
Abbo, Khalil, and Nehal Hameed. “New Hybrid Conjugate Gradient Method As a Convex Combination of Liu-Storey and Dixon Methods”. Journal of Multidisciplinary Modeling and Optimization, vol. 1, no. 2, Jan. 2019, pp. 91-99, https://izlik.org/JA37AX63CC.
Vancouver
1.Khalil Abbo, Nehal Hameed. New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. jmmo [Internet]. 2019 Jan. 1;1(2):91-9. Available from: https://izlik.org/JA37AX63CC