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Reseach Article

Modified Conjugate Gradient Method for Unconstrained Optimization

by Thamera K. Alkhashab
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 86 - Number 15
Year of Publication: 2014
Authors: Thamera K. Alkhashab
10.5120/15065-3509

Thamera K. Alkhashab . Modified Conjugate Gradient Method for Unconstrained Optimization. International Journal of Computer Applications. 86, 15 ( January 2014), 42-46. DOI=10.5120/15065-3509

@article{ 10.5120/15065-3509,
author = { Thamera K. Alkhashab },
title = { Modified Conjugate Gradient Method for Unconstrained Optimization },
journal = { International Journal of Computer Applications },
issue_date = { January 2014 },
volume = { 86 },
number = { 15 },
month = { January },
year = { 2014 },
issn = { 0975-8887 },
pages = { 42-46 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume86/number15/15065-3509/ },
doi = { 10.5120/15065-3509 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:04:20.200112+05:30
%A Thamera K. Alkhashab
%T Modified Conjugate Gradient Method for Unconstrained Optimization
%J International Journal of Computer Applications
%@ 0975-8887
%V 86
%N 15
%P 42-46
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Conjugate gradient method holds an important role in solving unconstrained Optimizations , especially for large scale problems. Numerous studies and modific ations have been done to improve this method . In this paper , we propose a new conjugate gradient meth od which is computed by modifying Dai and Yuan formula . This new formula for the denominator is introduced and the numerator of Dai and Yuan for mula is retrained , but still possesses global converge nce properties. Numerical results based on number of iterations and number of function evaluations by usin g exact line search have shown that the new formul a is an efficient when we comparative it with the oth er conjugate gradient methods.

References
  1. Al - Baali , M . (1985) . Descent Property and Global Convergence of Fletcher- Reeves Method with Inexact Line Search . IMA J . Numer . Anal. , 5, 121-124.
  2. Andrei, N. (2008). An Unconstrained Optimization Test Functions Collection. Advanced Modeling and Optimization, 10(1), 147-161.
  3. Andrei, N. (2009). Accelerated Conjugate Gradient algorithm with finite difference Hessian / vector product approximation for unconstrained optimization . J,Comput Appl. Math. 230,70-582
  4. Birgin, E. G. and Martinez. J. M. (2001). . A Spectral Conjugate Gradient Method for Unconstrained Optimization. J. Appl. Maths. Optim, 43,117-128.
  5. Dai, Y. and Yuan, Y. (1998) . Nonlinear Conjugate Gradient method . Shanghai Scientific and Technical Publishers, Beijing.
  6. Dai, Y. and Yuan, Y. (2000) . A Nonlinear Con-jugate Gradient with a Strong Global Convergence Properties. SIAM J. Optim. , 10, 177-182.
  7. Dai, Y. H. and Yuan, Y. (2002). A Note on The Nonlinear Conjugate Gradient Method. J,Comput. Appl. Math. , 18(6), 575-582.
  8. Dai, Y. H. , Han, J. Y. , Liu, G. H. , Sun, D. F. , Yin, X. and Yuan, Y. (1999). Convergence Properties of Properties of Nonlinear Conjugate Gradient Method. SIAM J. Optim. , 10, 348-358.
  9. Fletcher,R. and Reeves, C. (1964). Function Minimization by Conjugate Gradients. Comput. J. , 7, 149-154.
  10. Gilbert, J. C. and Nocedal, J. (1992). Global Convergence Properties of Conjugate Gradient Methods for optimization. SIAM J. Optim. , 2(1),21-42.
  11. Hager,W. W and Zhang, H. C. (2005). A New Conjugate Gradient Method with Guaranteed Descent and efficient line search. SIAM J. Optim. , 16, 170-192.
  12. Hestenes, M. R. and Steifel, E . (1952) . Method Of Conjugate Gradient for Solving Linear Equations. J,Res. Nat. Bur. Stand. , 49, 409-436.
  13. Liu,Y. and Storey, C. (1992). Efficient Generalized conjugate gradient algorithms part 1:theory. J,Comput. Appl. Math. , 69, 129-137.
  14. Mustafa Mamat , Mohd Rivaie , Islam Mohdand Muhammad Fauzi. (2010). A New Conjugate Gradient Coefficient for Unconstrained Optimization. Int. J. Contemp . Math . Sciences ,5(29),1429-1437.
  15. Polak , E. and , Ribiere, G. (1969). Note Sur La Convergence De Directions Conjugees. Rev. Francaise Informat Recherche Operationelle,3EAnnee(16), 35-43.
  16. Powell, M. J. D. (1986). Convergence Properties of Algorithm for Nonlinear Optimization. SIAM Review. , 28(4), 487-500.
  17. Rivaie. M , Fauzi. M, Mamat . M and Mohd . I . (2011). Modified Hestenes-Steifel Method forfor Unconstrained Optimization. J. Appl Sciences,11(8): DOI:10. 3923/jas. 2011. 1461-1464
  18. Shi, Z. J. and Gao, J. (2009). A New Family of,Conjugate Gradient Methods. J,Comput. Appl. Math. , 224, 444-457.
  19. Sun, J. and Zhang, J. (2001). Global Convergence of Conjugate Gradient Methods without Line Search. Annals. Opr. Rch, 103, 161-173.
  20. Touati-Ahmed, D. and Storey, C . (1990). Efficient Hybrid Conjugate Gradient Techniques, J. Optim. Theory Appl. , 64, 379-397.
  21. Wolfe, P. (1969) . Convergence Conditions for Ascent Method. SIAM Rev. ,11,226-235.
  22. Yuan, G and Wei, Z. (2009). New Line Search Methods for Unconstrained Optimization . J. Korean Stat. Soc. , 38, 29-39.
  23. Yuan, Y. and Sun,W. (1999). Theory and Methods of optimization. Science Press of China,Beijing.
  24. Zoutendijk, G. (1970). Nonlinear ProgrammingComputational Methods. In : Abadie J. (Ed. )Integer and nonlinear programming, 37-86. Received: November, 2009
Index Terms

Computer Science
Information Sciences

Keywords

Conjugate gradient methods global convergence unconstrained optimization exact line search