Global convergence of conjugate gradient method in unconstrained optimization problems
Abstract
In this study, we propose a new parameter in the conjugate gradient method. It is shown that the new method fulfils the sufficient descent condition with the strong Wolfe condition when inexact line search has been used. The numerical results of this suggested method also shown that this method outperforms to other standard conjugate gradient method.
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References
N. Andrei, Advanced Modeling and optimization 10, 147-161 (2008).
R. Fletcher and C. M. Reeves, The computer journal 7, 149-154 (1964). https://doi.org/10.1093/comjnl/7.2.149
E. Polak and G. Ribiere, Revue fran¸caise d'informatique et de recherche operationnelle. Serie rouge 3, 35-43 (1969). https://doi.org/10.1051/m2an/196903R100351
R. Fletcher, Practical methods of optimization (John Wiley & Sons, 2013).
Y. Liu and C. Storey, Journal of optimization theory and applications 69, 129-137 (1991). https://doi.org/10.1007/BF00940464
Z. Dai and F. Wen, Numerical Algorithms 59, 79-93 (2012). https://doi.org/10.1007/s11075-011-9477-2
M. J. D. Powell, Mathematical programming 12, 241-254 (1977). https://doi.org/10.1007/BF01593790
I. Bongartz, A. R. Conn, N. Gould, and P. L. Toint, ACM Transactions on Mathematical Software (TOMS) 21, 123-160 (1995). https://doi.org/10.1145/200979.201043
N. Andrei, Optimization methods and software 24, 89-104 (2009). https://doi.org/10.1080/10556780802393326
Y. H. Dai and Y. Yuan, SIAM Journal on optimization 10, 177-182 (1999).
https://doi.org/10.1137/S1052623497318992
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Vol. 49 (NBS Washington, DC, 1952). https://doi.org/10.6028/jres.049.044
G. Li, C. Tang, and Z. Wei, Journal of Computational and Applied Mathematics 202, 523-539 (2007).
https://doi.org/10.1016/j.cam.2006.03.005
Z. Wei, G. Li, and L. Qi, Applied Mathematics and Computation 175, 1156-1188 (2006). https://doi.org/10.1016/j.amc.2005.08.027
H. Yabe and N. Sakaiwa, Journal of the Operations Research Society of Japan 48, 284-296 (2005). https://doi.org/10.15807/jorsj.48.284
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