Some three-term conjugate gradient methods with the new direction structure

Published on Apr 1, 2020in Applied Numerical Mathematics2.468
路 DOI :10.1016/J.APNUM.2019.10.011
J.K. Liu1
Estimated H-index: 1
(CTGU: Chongqing Three Gorges University),
Y.X. Zhao1
Estimated H-index: 1
(CTGU: Chongqing Three Gorges University),
X.L. Wu1
Estimated H-index: 1
(CTGU: Chongqing Three Gorges University)
Sources
Abstract
Abstract In this paper, a three-term conjugate gradient method with the new direction structure is proposed for solving large-scale unconstrained optimization problems, which generates a sufficient descent direction in per-iteration by the aid of some inexact line search conditions. Under suitable assumptions, the proposed method is globally convergent for nonconvex smooth problems. We further generalize the new direction structure to other traditional methods and obtain some algorithms with the same structure as the proposed method. Preliminary numerical comparisons show that the proposed methods are effective and promising for the test problems.
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#2Tingting Li (Xida: Guangxi University)H-Index: 2
Last. Wujie Hu (Xida: Guangxi University)H-Index: 4
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Abstract Nonlinear systems present a quite complicate problem. As the number of dimensions increases, it becomes more difficult to find the solution of the problem. In this paper, a modified conjugate gradient method is designed that has a sufficient descent property and trust region property. It is interesting that the formula for search direction makes full use of the property of convex combination between the deepest descent algorithm and the classical LS conjugate gradient (CG) method. The g...
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#1J. K. Liu (CTGU: Chongqing Three Gorges University)H-Index: 2
#2J. 艁. Xu (CTGU: Chongqing Three Gorges University)H-Index: 1
Last. L. Q. Zhang (CTGU: Chongqing Three Gorges University)H-Index: 1
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ABSTRACTApplying Powell symmetrical technique to the Liu鈥揝torey conjugate gradient method, a partially symmetrical Liu鈥揝torey conjugate gradient method is proposed and extended to solve nonlinear m...
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#1Xiaoliang Dong (MUC: Minzu University of China)H-Index: 9
#2Ze-Xian Liu (Xidian University)H-Index: 3
Last. Xiang-Li Li (GUET: Guilin University of Electronic Technology)H-Index: 2
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A new three-term Hestenes鈥揝tiefel-type conjugate gradient method is proposed in which the search direction can satisfy the sufficient descent condition as well as an adaptive conjugacy condition. It is notable that search directions of the method are dynamically adjusted between that of the Newton method and the 3HS+ method, accelerating the convergence or reducing the condition number of iteration matrix. Under mild conditions, we show that the proposed method converges globally for general obj...
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#1Xiangli Li (GUET: Guilin University of Electronic Technology)H-Index: 6
#2Juanjuan Shi (GUET: Guilin University of Electronic Technology)H-Index: 1
Last. Jianglan Yu (GUET: Guilin University of Electronic Technology)H-Index: 1
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Abstract The spectral conjugate gradient method is an effective method for large-scale unconstrained optimization problems. In this paper, based on Quasi-Newton direction and Quasi-Newton equation, a new spectral conjugate gradient method is proposed. This method is motivated by the three-term modified Polak-Ribiyre-Polyak (PRP) method and spectral parameters. The global convergence of algorithm is proved for general functions under a strong Wolfe line search. Numerical results show that the new...
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#1Shummin Nakayama (Ridai: Tokyo University of Science)H-Index: 2
#2Yasushi NarushimaH-Index: 9
Last. Hiroshi YabeH-Index: 16
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Memoryless quasi-Newton methods are studied for solving large-scale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, ...
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#1Bakhtawar Baluch (UMT: Universiti Malaysia Terengganu)H-Index: 2
#2Zabidin Salleh (UMT: Universiti Malaysia Terengganu)H-Index: 11
Last. Ahmad Alhawarat (Isra University)H-Index: 5
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This paper describes a modified three-term Hestenes鈥揝tiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees glo...
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#1Xiaoliang Dong (North Minzu University)H-Index: 9
#2Deren Han (Beihang University)H-Index: 26
Last. Jianguang Zhu (SDUST: Shandong University of Science and Technology)H-Index: 1
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Abstract An accelerated three-term conjugate gradient method is proposed, in which the search direction can satisfy the sufficient descent condition as well as extended Dai鈥揕iao conjugacy condition. Different from the existent methods, a dynamical compensation strategy in our proposed method is considered, that is Li鈥揊ushikuma-type quasi-Newton equation is satisfied as much as possible, otherwise, to some extent, the singular values of iteration matrix of search directions will adaptively cluste...
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#2Yuming Feng (CTGU: Chongqing Three Gorges University)H-Index: 11
Last. Limin Zou (CTGU: Chongqing Three Gorges University)H-Index: 10
view all 3 authors...
The three-term conjugate gradient methods solving large-scale optimization problems are favored by many researchers because of their nice descent and convergent properties. In this paper, we extend some new conjugate gradient methods, and construct some three-term conjugate gradient methods. An remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition without any line search. Under the standard Wolfe line search, the global converg...
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#1Shengwei Yao (Guangxi University of Finance and Economics)H-Index: 1
#2Liangshuo Ning (Guangxi University of Finance and Economics)H-Index: 1
Abstract Due to its simplicity and low memory requirement, conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems. In this paper, we propose a three-term conjugate gradient method. The search direction is given by a symmetrical Perry matrix, which contains a positive parameter. The value of this parameter is determined by minimizing the distance of this matrix and the self-scaling memoryless BFGS matrix in the Frobenius norm. The sufficient descent...
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#1Gonglin Yuan (Xida: Guangxi University)H-Index: 8
#2Maojun Zhang (GUET: Guilin University of Electronic Technology)H-Index: 1
In this paper, a conjugate gradient algorithm for systems of large-scale nonlinear equations is designed by the following steps: (i) A three-terms conjugate gradient direction d k is presented where the direction possesses the sufficient descent property and the trust region property independent of line search technique; (ii) A backtracking line search technique along the direction is proposed to get the step length 伪 k and construct a point; (iii) If the point satisfies the given condition then...
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Abstract null null Billet production is for the most part completed in a continuous casting machine. To produce a billet of suitable quality, the secondary cooling control system needs to provide an appropriate value of water flow rate. At present, most secondary cooling control methods are based on a heat transfer model for the billet, the accuracy of which can directly impact the cooling effect and further affect its quality. In practice, it is difficult to determine the heat flux at the bille...
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#1Ahmad Alhawarat (UMT: Universiti Malaysia Terengganu)H-Index: 5
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#1Basim A. HassanH-Index: 4
#2Maulana MalikH-Index: 4
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The quasi-Newton (QN) method are among the efficient variants of conjugate gradient (CG) method for solving unconstrained optimization problems. The QN method utilizes the gradients of the function while ignoring the available value information at every iteration. In this paper, we extended the Dai-Yuan [39] coefficient in designing a new CG method for large-scale unconstrained optimization problems. An interesting feature of our method is that its algorithm not only uses the available gradient ...
#1Maulana Malik (UI: University of Indonesia)H-Index: 4
#2Auwal Bala Abubakar (Sefako Makgatho Health Sciences University)H-Index: 13
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Abstract Solidification heat transfer process of billet is described by nonlinear partial differential equation (PDE). Due to the poor productive environment, the boundary condition of this nonlinear PDE is difficult to be fixed. Therefore, the identification of boundary condition of two-dimensional nonlinear PDE is considered. This paper transforms the identification of boundary condition into a PDE optimization problem. The Lipchitz continuous of the gradient of cost function is proved based o...
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