A one-layer recurrent neural network for constrained nonconvex optimization

LiGuocheng,; Yan-zheng,; Wang, Jun

doi:10.1016/j.neunet.2014.09.009

Cited by 83 publications

(13 citation statements)

References 38 publications

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“…where γ > 0 is a penalty parameter, and sgn(•) is the sign function. Then, inspired by [14,22], we construct the following feedback neural network for minimizing E(x)ẋ = − ∇E(x)…”

Section: Problem Statement and Model Descriptionmentioning

confidence: 99%

“…Such a penalty γ can strengthen the constraints and make the results converge into the constraints more efficiently in optimization problems with inequality constraints. In addition, as we will show later, the penalty parameter γ makes the neural network feasible to fit in the network model for solving some nonconvex problems in [22].…”

Section: Problem Statement and Model Descriptionmentioning

confidence: 99%

“…In [21], a one-layer recurrent projection neural network was utilized for solving pseudoconvex optimization problems with general convex constraints. Li et al [22] provided a one-layer recurrent neural network based on an exact penalty function method for solving nonconvex optimization problems subject to general inequality constraints. Bian et al [23] proposed a one-layer recurrent neural network for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints.…”

Section: Introductionmentioning

confidence: 99%

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A Quantum-Behaved Neurodynamic Approach for Nonconvex Optimization with Constraints

Cai

Lou

2019

Algorithms

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This paper presents a quantum-behaved neurodynamic swarm optimization approach to solve the nonconvex optimization problems with inequality constraints. Firstly, the general constrained optimization problem is addressed and a high-performance feedback neural network for solving convex nonlinear programming problems is introduced. The convergence of the proposed neural network is also proved. Then, combined with the quantum-behaved particle swarm method, a quantum-behaved neurodynamic swarm optimization (QNSO) approach is presented. Finally, the performance of the proposed QNSO algorithm is evaluated through two function tests and three applications including the hollow transmission shaft, heat exchangers and crank–rocker mechanism. Numerical simulations are also provided to verify the advantages of our method.

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“…where γ > 0 is a penalty parameter, and sgn(•) is the sign function. Then, inspired by [14,22], we construct the following feedback neural network for minimizing E(x)ẋ = − ∇E(x)…”

Section: Problem Statement and Model Descriptionmentioning

confidence: 99%

Section: Problem Statement and Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Quantum-Behaved Neurodynamic Approach for Nonconvex Optimization with Constraints

Cai

Lou

2019

Algorithms

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“…The sparse constraint causes GSNMF to be a nonconvex nonsmooth problem, and traditional optimization algorithms can not be optimized directly. Recently, numerous neural networks have emerged as a powerful tool for optimization problems [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. For some nonconvex problems, an inertial projection neural network (IPNN) [16] has been proposed to search different local optimal solutions by the inertial term.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the SFLA framework, the global optimal solution can be searched. Moreover, there are many optimization methods for nonconvex nonsmooth problems that use neural networks [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Graph Sparse Nonnegative Matrix Factorization Algorithm Based on the Inertial Projection Neural Network

Dai

Xiang

2018

Complexity

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We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method.

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A cooperative neural dynamic model for solving general convex nonlinear optimization problems with fuzzy parameters and an application in manufacturing systems

Jahangiri,

Nazemi

2024

Adaptive Control & Signal

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SummaryIn the presented study, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is calculated using a recurrent neural network (RNN) model. Since there is a few research for solving FNLOP by RNN's, we give a new approach to solve the problem. By reducing the original program to an interval problem and then weighting problem, the Karush–Kuhn–Tucker (KKT) conditions are given. Moreover, we use the KKT conditions into a RNN as an important tool to solve the problem. Besides, the global convergence properties and the Lyapunov stability of the dynamic model are studied in this study. In the final step, some illustrative examples are considered to establish the obtained results. Reported results are compared with some others network models.

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A one-layer recurrent neural network for constrained nonconvex optimization

Cited by 83 publications

References 38 publications

A Quantum-Behaved Neurodynamic Approach for Nonconvex Optimization with Constraints

A Quantum-Behaved Neurodynamic Approach for Nonconvex Optimization with Constraints

Graph Sparse Nonnegative Matrix Factorization Algorithm Based on the Inertial Projection Neural Network

A cooperative neural dynamic model for solving general convex nonlinear optimization problems with fuzzy parameters and an application in manufacturing systems

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