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Year 2018, Volume: 1 Issue: 2, 91 - 99, 21.01.2019

Abstract

References

  • [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

Year 2018, Volume: 1 Issue: 2, 91 - 99, 21.01.2019

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. 

References

  • [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.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Khalil Abbo This is me

Nehal Hameed This is me

Publication Date January 21, 2019
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

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. January 2019;1(2):91-99.
Chicago 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 1, no. 2 (January 2019): 91-99.
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 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, 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 (January 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 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, 2019, pp. 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.