A new Modification of the Quasi-Newton Method for Unconstrained Optimization

Huda Issam Ahmed, Eman T. Hamed, Hamsa Th. Saeed Chilmeran, Abbas Y. Al-Bayati

Abstract


In this work A new conjugate gradient method (CG) suggested which is a linear combination between Hager- Zhang [HZ] and Dai-Liao m-Technique; convex function; BFGS method; convergence analysis. method [DL]. Also, we use this proposed method to a modified of BFGS method and prove the positive definite and QN- condition. The numerical experiments show that the propose method is promising. which can confirm that the direction is satisfied a descent direction. Under some conditions, we have proved that the new search is globally convergent by using the strong Wolfe condition. The preliminary numerical results show that our new technique outperforms compared to alternative methods on depending Dolan-Mor'e performance profile".

In this work A new conjugate gradient method (CG) suggested which is a linear combination between Hager- Zhang [HZ] and Dai-Liao m-Technique; convex function; BFGS method; convergence analysis. method [DL]. Also, we use this proposed method to a modified of BFGS method and prove the positive definite and QN- condition. The numerical experiments show that the propose method is promising. which can confirm that the direction is satisfied a descent direction. Under some conditions, we have proved that the new search is globally convergent by using the strong Wolfe condition. The preliminary numerical results show that our new technique outperforms compared to alternative methods on depending Dolan-Mor'e performance profile".

 


Keywords


Conjugate gradient method; Unconstrained optimization; convex function; BFGS method; Strong Wolfe condition; Globally convergence; Dolan-Mor'e performance.

References


M.R. Hestense and E.l. Stiefel, Methods of conjugate gradients for solving linear system, J. Research Nat.Bur. Standards, 49, 1952, pp. 409-436.

R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Comput. J.,7, 1964, pp.149-154.

E. Polak, and G Ribiere, Note sur la convergence de methods de directions conjugate'e, Rev. Francaise In format. Recherché Ope'rtionelle ,3,1969, pp.35-43.

B.T. Polaak, The conjugate gradient method in extreme problems, USSR comp. Math. and Math Phys.,9,1969, pp.94-112.

Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. on Optim., 10, 1999, pp.177-182.

Y. H. Dai and L.Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim.,43, 2001, pp. 87-101.

W.W Hager and Zhang ,Anew conjugate gradient method with guaranteed descent and an efficient Line search ,SIAM J. Optim.,16,2005,pp.170-192.

W.W Hager and Zhang ,A Survey of nonlinear conjugate gradient methods, Pacific J.Optim.,2, 2006, pp.35-58.

E. T. Hamed, H. I. Ahmed,and A. Y. Al-Bayati, “A New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization,” Journal of Applied Mathematics, vol. 2019, 2019. ‏. https://doi.org/10.1155/2019/8728196.

M. K. Dauda, M. Mamat, M. A. Mohamed and N. S. A. Hamzah, “Hybrid conjugate gradient parameter for solving symmetric systems of nonlinear equations,”Indonesian Journal of Electrical Engineering and Computer Science. vol. 16, no. 1, 2019, pp. 539-543. DOI: 10.11591/ijeecs.v16.i1.pp539-543

E.T. Hamed,R.Z. Al-Kawaz and A.Y.Al- Bayati, “New investigation for the Liu-Story scaled conjugate gradient method for nonlinear optimization,”Hindawi J. Math, vol. 2020, 2020. https://doi.org/10.1155/2020/3615208.

H.I. Ahmed, R.Z.Al-Kawaz and A.Y. Al- Bayati, “Spectral three-term constrained conjugate gradient algorithm for function minimizations,”Hindawi J. Appl. Math., vol 2019, 2019. https://doi.org/10.1155/2019/6378368.

E.T. Hamed, H.I.Ahmed, H. Y. Najm, “Global Convergence of Conjugate Gradient Method in Unconstrained Optimization Problems,”International Conference of Mathematical Sciences (ICMS 2018) AIP Conf. Proc. 2086, 030029-1– 030029-4; https://doi.org/10.1063/1.5095114,Published by AIP Publishing. 978-0-7354-1816-5

B. A.Hassan, H. O.Dahawi and A. S. Younus, “A new kind of parameter conjugate gradient for unconstrained optimization,”Indonesian Journal of Electrical Engineering and Computer Science,vol. 17, no. 1, pp. 404-411, B. A

Hassan, Z. M. Abdullah, H. N. Jabbar, “A descent extension of the Dai - Yuan conjugate gradient technique,”Indonesian Journal of Electrical Engineering and Computer Science.vol. 16, no. 2, November 2019, pp. 661-668. DOI:

11591/ijeecs.v16.i2.pp661-668.

C. Ahmed and B. Taher, “A new modification nonlinear conjugate gradient method with strong wolf-powell line search,”Indonesian Journal of Electrical Engineering and Computer Science.vol. 18, no. 1, April 2020, pp. 525-532,

DOI:10.11591/ijeecs.v18.i1.pp525-532 .

N. S. Mohamed, M. Mamat, M.Rivaie, S. M.Shaharudin, “A new hybrid coefficient of conjugate gradient method,”Indonesian Journal of Electrical Engineering and Computer Science.vol. 18, no. 3, June 2020, pp. 1454-1463,

DOI: 10.11591/ijeecs.v18.i3.pp1454-1463.2020.

Y.H. Dai, Han, J.Y., Liu, G.H., Sun, D.F., Yin, .X. and Yuan, Y., Convergence properties of Nonlinear conjugate gradient methods. SIAM Jurnal on Optimization 10, 1999, 348-358.

R. Ghanbari., S .Babaie–kafaki, An A dative Hager-Zhang Conjugate Gradient Method ,Faculty of sciences Mathematics,2016, pp.3715-3723.

Yabe, H., and Takano, M., Global convergence properties of new nonlinear conjugate gradient methods for unconstrained optimization, Computational Optimization and Application,28, 2004, pp.203-225.

J.M. Perry .A class of conjugate gradient algorithms with a two–step variable-metric Discussion paper 269 ,Center for Mathematical Studies in Economics and Management Science, Northwestern University,Evanston ,I I Illinois,1977.

D.F. Shanno ,On the convergence of anew conjugate gradient algorithm ,SIAMJ. Number .Anal. , 1978;pp.1247-1257.

N. Andrei, An unconstrained optimization test functions collection, Advanced Modeling and Optimization, the Electronic International Journal VoL.10,no,L, 2008, pp.147-161.

N. Andrei, Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization Bulletin of the Malaysian Mathematical Science Society. second series ,vol.34,na2,2011, pp.319-330.

E. D. Dolan and J. J. Mor'e, Benchmarking optimization software with performance profiles, Mathematical Programming, vol. 91, no. 2, 2002, pp. 201–213.




DOI: http://doi.org/10.11591/ijeecs.v21.i1.pp%25p
Total views : 7 times

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

shopify stats IJEECS visitor statistics