Conjugate gradient methods (CG) are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new conjugate gradient method for unconstrained optimization. This method is a convex combination of Fletcher and Reeves (abbreviated FR), Polak–Ribiere–Polyak (abbreviated PRP) and Dai and Yuan (abbreviated DY) methods. The new conjugate gradient methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for this method. The numerical experiments are done to test the efficiency of the proposed method, which confirms its promising potentials.
Keywords: Unconstrained optimization, hybrid conjugate gradient method, sufficient descent, convex combination, global convergence
@article{RO_2022__56_4_2315_0,
author = {Ben Hanachi, Sabrina and Sellami, Badreddine and Belloufi, Mohammed},
title = {New iterative conjugate gradient method for nonlinear unconstrained optimization},
journal = {RAIRO. Operations Research},
pages = {2315--2327},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/ro/2022109},
mrnumber = {4458849},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022109/}
}
TY - JOUR AU - Ben Hanachi, Sabrina AU - Sellami, Badreddine AU - Belloufi, Mohammed TI - New iterative conjugate gradient method for nonlinear unconstrained optimization JO - RAIRO. Operations Research PY - 2022 SP - 2315 EP - 2327 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022109/ DO - 10.1051/ro/2022109 LA - en ID - RO_2022__56_4_2315_0 ER -
%0 Journal Article %A Ben Hanachi, Sabrina %A Sellami, Badreddine %A Belloufi, Mohammed %T New iterative conjugate gradient method for nonlinear unconstrained optimization %J RAIRO. Operations Research %D 2022 %P 2315-2327 %V 56 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022109/ %R 10.1051/ro/2022109 %G en %F RO_2022__56_4_2315_0
Ben Hanachi, Sabrina; Sellami, Badreddine; Belloufi, Mohammed. New iterative conjugate gradient method for nonlinear unconstrained optimization. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2315-2327. doi: 10.1051/ro/2022109
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