Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 1 Sayı: 2, 91 - 99, 21.01.2019

Öz

Kaynakça

  • [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.

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

Yıl 2018, Cilt: 1 Sayı: 2, 91 - 99, 21.01.2019

Öz

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. 

Kaynakça

  • [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.
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Khalil Abbo Bu kişi benim

Nehal Hameed Bu kişi benim

Yayımlanma Tarihi 21 Ocak 2019
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

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.
AMA Abbo K, Hameed N. New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. jmmo. Ocak 2019;1(2):91-99.
Chicago Abbo, Khalil, ve Nehal Hameed. “New Hybrid Conjugate Gradient Method As a Convex Combination of Liu-Storey and Dixon Methods”. Journal of Multidisciplinary Modeling and Optimization 1, sy. 2 (Ocak 2019): 91-99.
EndNote Abbo K, Hameed N (01 Ocak 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 K. Abbo ve N. Hameed, “New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods”, jmmo, c. 1, sy. 2, ss. 91–99, 2019.
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 (Ocak 2019), 91-99.
JAMA 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 ve Nehal Hameed. “New Hybrid Conjugate Gradient Method As a Convex Combination of Liu-Storey and Dixon Methods”. Journal of Multidisciplinary Modeling and Optimization, c. 1, sy. 2, 2019, ss. 91-99.
Vancouver Abbo K, Hameed N. New Hybrid Conjugate Gradient Method as a Convex Combination of Liu-Storey and Dixon Methods. jmmo. 2019;1(2):91-9.