A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix
Keywords:Conjugate gradient, Descent condition, global convergent, Numerical results.
AbstractIn this paper, a new type nonlinear conjugate gradient method based on the Scale
Matrix 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.
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.
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.
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.
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.
Hestenes, M. R. and Stiefel E. L. (1952) ' Method of conjugate gradients for solving linear systems' J. Research Nat. Standards 49, pp.409-436.
Liu Y. and Storey C. (1991) ' Efficient generalized conjugate gradients algorithms ' Part 1 : Theory. J. Optimization Theory and Applications 69, pp.129-137.
Nocedal J. and Wright S. J. (1999). Numerical Optimization. Springer. New York.
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.
How to Cite
The journal has no restrictions for the author to hold the copyrights of his articles. The journal does not allow authors to republish the same article in other journals or conferences that is published in one of its volumes.