A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

Zheng, Lianxi; Yang, Lei; Liang, Yong

doi:10.1109/access.2020.2990298

Cited by 21 publications

(17 citation statements)

References 59 publications

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“…We notice that modified spectral gradient algorithms were proposed in [33,34] for solving problem (1), but our algorithm is very different from theirs in the following aspects. Firstly, we give a changeable choice for the inexact parameter in the spectral method.…”

Section: Introductionmentioning

confidence: 90%

A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint

Lin

2020

Mathematical Problems in Engineering

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In this paper, we propose a family of modified spectral projection methods for nonlinear monotone equations with convex constraints, where the spectral parameter is mainly determined by a convex combination of the modified long Barzilai–Borwein stepsize and the modified short Barzilai–Borwein stepsize. We obtain a trial point by the spectral method and then get the iteration point by the projection technique. The algorithm can generate a bounded iterative sequence automatically, and we obtain the global convergence of the proposed method in the sense that every limit point is a solution of the nonlinear equation. The proposed method can be used to resolve the large-scale nonlinear monotone equations with convex constraints including smooth and nonsmooth equations. Numerical results for nonlinear equation problems and the ℓ 1 -norm regularization problem in compressive sensing demonstrate the efficiency and efficacy of our method.

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Section: Introductionmentioning

confidence: 90%

A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint

Lin

2020

Mathematical Problems in Engineering

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“…In ordinary machine learning, convex generally means that the parameters are convex, and thus the weights are convex [40,52]. The convexity of convex neural networks means that the output is convex with respect to the input, while the network parameters are not fully convex.…”

Section: Convex Neural Network Structure Designmentioning

confidence: 99%

Convex Neural Networks Based Reinforcement Learning for Load Frequency Control under Denial of Service Attacks

Zeng

Zhu

et al. 2022

Algorithms

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With the increase in the complexity and informatization of power grids, new challenges, such as access to a large number of distributed energy sources and cyber attacks on power grid control systems, are brought to load-frequency control. As load-frequency control methods, both aggregated distributed energy sources (ADES) and artificial intelligence techniques provide flexible solution strategies to mitigate the frequency deviation of power grids. This paper proposes a load-frequency control strategy of ADES-based reinforcement learning under the consideration of reducing the impact of denial of service (DoS) attacks. Reinforcement learning is used to evaluate the pros and cons of the proposed frequency control strategy. The entire evaluation process is realized by the approximation of convex neural networks. Convex neural networks are used to convert the nonlinear optimization problems of reinforcement learning for long-term performance into the corresponding convex optimization problems. Thus, the local optimum is avoided, the optimization process of the strategy utility function is accelerated, and the response ability of controllers is improved. The stability of power grids and the convergence of convex neural networks under the proposed frequency control strategy are studied by constructing Lyapunov functions to obtain the sufficient conditions for the steady states of ADES and the weight convergence of actor–critic networks. The article uses the IEEE14, IEEE57, and IEEE118 bus testing systems to verify the proposed strategy. Our experimental results confirm that the proposed frequency control strategy can effectively reduce the frequency deviation of power grids under DoS attacks.

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“…The proposed two-direction algorithm was compared to the modified spectral gradient projection (MSGP) algorithm [23] and the derivative-free spectral projection (DFSP) [24]. Furthermore, for the proposed algorithm, we set the starting parameters as follows: a = 0.1, g = 0.0001, c = 0.99, b = 1, and epsilon = 10 −9 .…”

Section: Application To the Monotone Nonlinear Equationsmentioning

confidence: 99%

“…Table 1. Numerical comparison of SDYCG algorithm versus DFSP [24], and MSGP algorithms [23]. Moreover, for Problem 3, the proposed algorithm won in terms of the minimum ITER, FEV, and CPU time.…”

Section: Application To the Monotone Nonlinear Equationsmentioning

confidence: 99%

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

et al. 2022

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In this paper, we propose two scaled Dai–Yuan (DY) directions for solving constrained monotone nonlinear systems. The proposed directions satisfy the sufficient descent condition independent of the line search strategy. We also reasonably proposed two different relations for computing the scaling parameter at every iteration. The first relation is proposed by approaching the quasi-Newton direction, and the second one is by taking the advantage of the popular Barzilai–Borwein strategy. Moreover, we propose a robust projection-based algorithm for solving constrained monotone nonlinear equations with applications in signal restoration problems and reconstructing the blurred images. The global convergence of this algorithm is also provided, using some mild assumptions. Finally, a comprehensive numerical comparison with the relevant algorithms shows that the proposed algorithm is efficient.

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A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

Cited by 21 publications

References 59 publications

A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint

A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint

Convex Neural Networks Based Reinforcement Learning for Load Frequency Control under Denial of Service Attacks

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

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