A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations

Guan, Hongbo; Wang, Sheng

doi:10.1155/2021/9919595

Mathematical Problems in Engineering

2021

DOI: 10.1155/2021/9919595

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A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations

Hongbo Guan

Sheng Wang

Abstract: In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method for solving large-scale nonlinear equations. Under weaker conditions, we show that the proposed method is globally convergent. We also carry out some numerical experiments to test the proposed method. The results show that the proposed method is efficient and stable.

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Cited by 2 publications

References 27 publications

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Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

Mtagulwa,

Kaelo,

Diphofu

et al. 2024

Journal of Applied Mathematics, Statistics and Informatics

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In this paper, we propose a modification that improves efficiency, robustness and reliability of the famous HS conjugate gradient method. In particular, we propose a hybrid of the HS and DHS methods, where DHS is another recent modification of the HS method. Irrespective of the line search, the search direction of the proposed method is sufficiently descent. Moreover, the new approach guarantees global convergence for general functions under the strong Wolfe line search. Numerical results and performance profiles are reported, and indicate that the new approach outperforms three similar methods in the literature. We also give a practical application of the new approach in minimizing risk in portfolio selection.

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Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

Mtagulwa,

Kaelo,

Diphofu

et al. 2024

Journal of Applied Mathematics, Statistics and Informatics

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A scaled Polak-Ribi$ \grave{e} $re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control

Sabi’u

Althobaiti

et al. 2023

MATH

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<abstract><p>This paper proposes Polak-Ribi$ \grave{e} $re-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi-Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator.</p></abstract>

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A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations

Cited by 2 publications

References 27 publications

Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

A scaled Polak-Ribi$ \grave{e} $re-Polyak conjugate gradient algorithm for constrained nonlinear systems and motion control

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