Some new three-term Hestenes–Stiefel conjugate gradient methods with affine combination

Xiang, Dong; Han, Deren; Ghanbari, Reza; Li, Xiangli; Dai, Zhifeng

doi:10.1080/02331934.2017.1295242

Cited by 21 publications

(11 citation statements)

References 38 publications

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“…In addition, for large-scale unconstrained optimization problems, the conjugate gradient method (CG) is another easy but effective method, due to the two attractive features: one is the low memory requirement, the other is strong global convergence properties. In recent years, the conjugate gradient method has achieved rich results (see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]) from the perspective of the sufficient descent property, qausi-Newton direction and conjugacy condition. Inspired by the extension of spectral gradient method to nonlinear monotone equations, CG methods have been applied in solving the nonlinear monotone equations problem.…”

Section: Introductionmentioning

confidence: 99%

A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Dai

Zhu

2020

Mathematics

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The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F. A globally convergent inexact Newton method for systems of monotone equations, in: M. Fukushima, L. Qi (Eds.)Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers. 1998, 355-369) and the modified Hestenes-Stiefel method in Dai and Wen (Dai, Z.; Wen, F. Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. Numer Algor. 2012, 59, 79-93). In addition, we propose a new line search for the derivative-free method. Global convergence of the proposed method is established if the system of nonlinear equations are Lipschitz continuous and monotone. Preliminary numerical results are given to test the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Dai

Zhu

2020

Mathematics

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“…However, it can be observed that the direction defined using ( 7)- (10) may not be of descent if the objective function f is given by (6). Based on this observation, we recall the nonmonotone derivative-free backtracking line search for computing the steplength.…”

Section: Algorithmmentioning

confidence: 99%

A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations

Hassan¹

2022

Preprint

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We present a multivariate spectral hybridization of Hestenes-Stiefel (HS) and Polak-Ribière-Polyak (PRP) method for solving large-scale nonlinear systems of equations. The search direction of the method is obtained by incorporating a multivariate spectral approach with the positive hybridization of Hestenes-Stiefel and Polak-Ribière-Polyak parameters (HS & PRP hybrid+). By employing a derivative-free nonmonotone line search technique, the global convergence of the sequence generated by the method is proven. Numerical experiments are given to demonstrate the good performance of the method compared with similar methods in the literature designed for solving large-scale nonlinear systems of equations.

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“…For the first time, the general three-term conjugate gradient (TTCG) methods were proposed by Beale [7] to solve the unconstrained optimization problems. In this approach, the search direction [2,6,26], the descent and conjugacy properties [4,11] and the sufficient descent and conjugacy properties [13,14]. A comparison between some TTCG methods is reported for solving unconstrained optimization problems, see [5].…”

Section: Introductionmentioning

confidence: 99%

Some generalized three-term conjugate gradient methods based on CD approach for unconstrained optimization problems

Arman¹,

Xu²,

Liu³

2021

Technium

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In this paper, based on the efficient Conjugate Descent (CD) method, two generalized CD algorithms are proposed to solve the unconstrained optimization problems. These methods are three-term conjugate gradient methods which the generated directions by using the conjugate gradient parameters and independent of the line search satisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search, the global convergence of the proposed methods are proved. Also, the preliminary numerical results on the CUTEst collection are presented to show effectiveness of our methods.

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Some new three-term Hestenes–Stiefel conjugate gradient methods with affine combination

Cited by 21 publications

References 38 publications

A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations

Some generalized three-term conjugate gradient methods based on CD approach for unconstrained optimization problems

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