Global convergence of conjugate gradient method in unconstrained optimization problems
DOI:
https://doi.org/10.5269/bspm.v38i7.46490Abstract
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.
References
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2. R. Fletcher and C. M. Reeves, The computer journal 7, 149-154 (1964). https://doi.org/10.1093/comjnl/7.2.149
3. 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
4. R. Fletcher, Practical methods of optimization (John Wiley & Sons, 2013).
5. Y. Liu and C. Storey, Journal of optimization theory and applications 69, 129-137 (1991). https://doi.org/10.1007/BF00940464
6. Z. Dai and F. Wen, Numerical Algorithms 59, 79-93 (2012). https://doi.org/10.1007/s11075-011-9477-2
7. M. J. D. Powell, Mathematical programming 12, 241-254 (1977). https://doi.org/10.1007/BF01593790
8. 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
9. N. Andrei, Optimization methods and software 24, 89-104 (2009). https://doi.org/10.1080/10556780802393326
10. Y. H. Dai and Y. Yuan, SIAM Journal on optimization 10, 177-182 (1999).
https://doi.org/10.1137/S1052623497318992
11. 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
12. 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
13. 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
14. 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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2019-10-14
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