Some modified Yabe–Takano conjugate gradient methods with sufficient descent condition
Dong, Xiao Liang1 ; Li, Wei Jun2 ; He, Yu Bo3
1 School of Mathematics and Information science, Beifang University of Nationalities, No. 204 North Wenchang Rd,Yinchuan, Ningxia 750021, P.R. China.
2 Network Information Technology Center, Beifang University of Nationalities, No. 204 North Wenchang Rd, Yinchuan, Ningxia 750021, P.R. China.
3 Department of Mathematics and Applied Mathematics, Huaihua University, No. 612 Yingfeng East Road, Huaihua, Hunan 418008, P.R. China.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 67-77.

Descent condition is a crucial factor to establish the global convergence of nonlinear conjugate gradient method. In this paper, we propose some modified Yabe–Takano conjugate gradient methods, in which the corresponding search directions always satisfy the sufficient descent property independently of the convexity of the objective function. Differently from the existent methods, a new update strategy in constructing the search direction is proposed to establish the global convergence of the presented methods for the general nonconvex objective function. Numerical results illustrate that our methods can efficiently solve the test problems and therefore is promising.

DOI : 10.1051/ro/2016028
Classification : 49M37, 65K05, 90C53
Mots-clés : Yabe–Takano conjugate gradient method, global convergence, sufficient descent condition, conjugacy condition, numerical comparison
Dong, Xiao Liang 1 ; Li, Wei Jun 2 ; He, Yu Bo 3

1 School of Mathematics and Information science, Beifang University of Nationalities, No. 204 North Wenchang Rd,Yinchuan, Ningxia 750021, P.R. China.
2 Network Information Technology Center, Beifang University of Nationalities, No. 204 North Wenchang Rd, Yinchuan, Ningxia 750021, P.R. China.
3 Department of Mathematics and Applied Mathematics, Huaihua University, No. 612 Yingfeng East Road, Huaihua, Hunan 418008, P.R. China. 
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     author = {Dong, Xiao Liang and Li, Wei Jun and He, Yu Bo},
     title = {Some modified {Yabe{\textendash}Takano} conjugate gradient methods with sufficient descent condition},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Dong, Xiao Liang; Li, Wei Jun; He, Yu Bo. Some modified Yabe–Takano conjugate gradient methods with sufficient descent condition. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 67-77. doi : 10.1051/ro/2016028. http://www.numdam.org/articles/10.1051/ro/2016028/

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