A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix
DOI:
https://doi.org/10.23851/mjs.v27i5.170Keywords:
Conjugate gradient, Descent condition, global convergent, Numerical results.Abstract
In this paper, a new type nonlinear conjugate gradient method based on the ScaleMatrix is derived. The new method has the decent and globally convergent
properties under some assumptions. Numerical results indicate the efficiency of
this method to solve the given test problems.
Downloads
References
Andrie N. (2008) ' An Unconstrained Optimization Test functions collection ' Advanced Modeling and optimization. 10, pp.147-161.
Barzilai. J. Borwein. J. M. (1988). Two point step size gradient method IMA J.Numer Numer. Anal. 8, pp. 141–148.
https://doi.org/10.1093/imanum/8.1.141
Cao W. and Wang K. (2010) ' Global convergence of a new conjugate gradient method for modified Liu-Storey formula' Journal of East China Normal University (Natural Science), 1, pp.44-51.
Dai Y. and Liao Z. (2001). New conjugate conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43, pp. 87-101.
https://doi.org/10.1007/s002450010019
Dai, Y. and Yuan Y. (1999) ' A non-linear conjugate gradients method with a strong global convergence property' SIAM J. Optimization,10, pp.177-182.
https://doi.org/10.1137/S1052623497318992
Fletcher, R. (1987) ' Practical Methods of Optimization (second edition). John Wiley and Sons, New York.
Fletcher, R. and Reeves C. (1964) ' Function minimization by conjugate gradients ' Computer J. 7, pp.149-154.
https://doi.org/10.1093/comjnl/7.2.149
Hestenes, M. R. and Stiefel E. L. (1952) ' Method of conjugate gradients for solving linear systems' J. Research Nat. Standards 49, pp.409-436.
https://doi.org/10.6028/jres.049.044
Liu Y. and Storey C. (1991) ' Efficient generalized conjugate gradients algorithms ' Part 1 : Theory. J. Optimization Theory and Applications 69, pp.129-137.
https://doi.org/10.1007/BF00940464
Nocedal J. and Wright S. J. (1999). Numerical Optimization. Springer. New York.
https://doi.org/10.1007/b98874
Polak, E. and Ribiere, G. (1969) ' Note for Convergence Direction Conjugate, Revue Francaise Informant, Research. Operational, 16, 35-43.
Zoutendijk G., 1970. Nonlinear Porgramming, computational methods, in: Integr and Nonlinear Programming, North-Holland, Amsterdam, pp. 37-86.
Yasushi N. and Hideaki I., (2011). Conjugate gradient methods using value of objective function for unconstrained optimization Optimization Letters, V.6, Issue 5, 941-955.
Downloads
Key Dates
Published
Issue
Section
License
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.