An efficient projection-based algorithm without Lipschitz continuity for large-scale nonlinear pseudo-monotone equations

Liu, J.K.; Lu, Zuliang; Xu, Jinming; Wu, Shih-Ching; Tu, Zhengwen

doi:10.1016/j.cam.2021.113822

Cited by 14 publications

(4 citation statements)

References 18 publications

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“…We denote the proposed Algorithm 1 by WF, and compare with some existing algorithms. Te conjugate gradient method in [35,36,37,38] are denoted by JKL, EMDY, PDY, and HG, respectively. Tese are derivative-free methods, where JKL and EMDY methods are the state-of-the-art methods.…”

Section: Numerical Resultsmentioning

confidence: 99%

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

Fang

Wang

Ding

2022

Journal of Mathematics

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In this study, we propose a new modified hybrid conjugate gradient projection method with a new scale parameter φ k for solving large-scale nonlinear monotone equations. The proposed method includes two major features: projection techniques and sufficient descent property independent of line search technique. Global convergence of the proposed method is proved under some suitable assumptions. Finally, numerical results illustrating the robustness of the suggested strategy and its comparisons are shown.

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Section: Numerical Resultsmentioning

confidence: 99%

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

Fang

Wang

Ding

2022

Journal of Mathematics

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“…In Ref. 16 , a projection-based method is proposed to solve large-scale nonlinear pseudo-monotone equations, without Lipschitz continuity. In Refs.…”

Section: Introductionmentioning

confidence: 99%

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

Hu,

Wu,

Yuan

2024

Sci Rep

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This paper introduces two three-term trust region conjugate gradient algorithms, TT-TR-WP and TT-TR-CG, which are capable of converging under non-Lipschitz continuous gradient functions without any additional conditions. These algorithms possess sufficient descent and trust region properties, and demonstrate global convergence. In order to assess their numerical performance, we compare them with two classical algorithms in terms of restoring noisy gray-scale and color images as well as solving large-scale unconstrained problems. In restoring noisy gray-scale images, we set the performance of TT-TR-WP as the standard, then TT-TR-CG takes around 2.33 times longer. The other algorithms around 2.46 and 2.41 times longer, respectively. In solving the same color images, the proposed algorithms exhibit relative good performance over other algorithms. Additionally, TT-TR-WP and TT-TR-CG are competitive in unconstrained problems, and the former has wide applicability while the latter has strong robustness. Moreover, the proposed algorithms are both more outstanding than the baseline algorithms in terms of applicability and robustness.

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“…Therefore, this work will only focus on the DFP methods, such as spectral gradient projection methods 7,8 and conjugate gradient projection (CGP) methods. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] The inertial step is a strategy that involves using information from the previous two iterations to calculate the current iteration, and it is one of the most effective methods for accelerating the convergence of iterative methods. This idea was originally proposed by Polyak, 28 who was inspired by an implicit discretization of a second-order-in-time dissipative dynamical system, represented by…”

Section: Introductionmentioning

confidence: 99%

“…Due to their derivative‐free nature, the latter has attracted significant attention. Therefore, this work will only focus on the DFP methods, such as spectral gradient projection methods 7,8 and conjugate gradient projection (CGP) methods 9‐27 …”

Section: Introductionmentioning

confidence: 99%

A family of inertial‐based derivative‐free projection methods with a correction step for constrained nonlinear equations and their applications

Liu,

Shao,

Yuan

et al. 2023

Numerical Linear Algebra App

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Numerous attempts have been made to develop efficient methods for solving the system of constrained nonlinear equations due to its widespread use in diverse engineering applications. In this article, we present a family of inertial‐based derivative‐free projection methods with a correction step for solving such system, in which the selection of the derivative‐free search direction is flexible. This family does not require the computation of corresponding Jacobian matrix or approximate matrix at every iteration and possess the following theoretical properties: (i) the inertial‐based corrected direction framework always automatically satisfies the sufficient descent and trust region properties without specific search directions, and is independent of any line search; (ii) the global convergence of the proposed family is proven under a weaker monotonicity condition on the mapping , without the typical monotonicity or pseudo‐monotonicity assumption; (iii) the results about convergence rate of the proposed family are established under slightly stronger assumptions. Furthermore, we propose two effective inertial‐based derivative‐free projection methods, each embedding a specific search direction into the proposed family. We present preliminary numerical experiments on certain test problems to demonstrate the effectiveness and superiority of the proposed methods in comparison with existing ones. Additionally, we utilize these methods for solving sparse signal restorations and image restorations in compressive sensing applications.

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An efficient projection-based algorithm without Lipschitz continuity for large-scale nonlinear pseudo-monotone equations

Cited by 14 publications

References 18 publications

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity

A family of inertial‐based derivative‐free projection methods with a correction step for constrained nonlinear equations and their applications

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