A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations

Xia, Youshen; Feng, Gang; Wang, Jun

doi:10.1016/j.neunet.2004.05.006

Cited by 159 publications

(47 citation statements)

References 11 publications

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“…Theoretically, the -WTA network (21) as well as network (18) do not need to choose any parameter (the scaling factor can be any positive number), which can be deemed as a great advantage over networks (15) and (16). In addition, the two networks (18) and (21) allow for some equal input signals [see (17)], a situation often encountered in practice but excluded by (15) and (16).…”

Section: Model Comparisonsmentioning

confidence: 99%

“…Then, we compare the structural complexities of the four -WTA networks (15), (16), (18), and (21). Because all of them are of complexity, it is necessary to give a more accurate estimation of the number of elements in them.…”

Section: Model Comparisonsmentioning

confidence: 99%

“…The other three networks can be analyzed in the same way by paying attention to the following two points. First, when counting the number of adders in (18), one should keep in mind that the items and need to be calculated once only though they appear at several places. Second, for the sake of fairness, when counting the number of multipliers in (15), the circuit parameters are not taken into account, and each sigmoid function is roughly defined to entail two adders and three multipliers for a quantitative comparison.…”

Section: Model Comparisonsmentioning

confidence: 99%

“…If is positive definite, several other salient networks are available for solving (1), e.g., [18]- [20], and [32]. The networks in [18] and [19] both suffer from the same difficulties as the networks in [12] and [15], while the network developed in [32], [20] does not, which is called extended projection neural network (8) where is a scaling factor.…”

mentioning

confidence: 99%

“…The networks in [18] and [19] both suffer from the same difficulties as the networks in [12] and [15], while the network developed in [32], [20] does not, which is called extended projection neural network (8) where is a scaling factor.…”

mentioning

confidence: 99%

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A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

Zhang

2009

IEEE Trans. Neural Netw.

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Abstract-In this paper, a new recurrent neural network is proposed for solving convex quadratic programming (QP) problems. Compared with existing neural networks, the proposed one features global convergence property under weak conditions, low structural complexity, and no calculation of matrix inverse. It serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems. In addition, it is found that by some variable substitution, the proposed network turns out to be an existing model for solving minimax problems. In this sense, it can be also viewed as a special case of the minimax neural network. Based on this scheme, a -winners-take-all ( -WTA) network with ( ) complexity is designed, which is characterized by simple structure, global convergence, and capability to deal with some ill cases. Numerical simulations are provided to validate the theoretical results obtained. More importantly, the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line. IndexTerms-Asymptotic stability, -winners-take-all ( -WTA), linear programming, neural network, quadratic programming.

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Section: Model Comparisonsmentioning

confidence: 99%

Section: Model Comparisonsmentioning

confidence: 99%

Section: Model Comparisonsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

Zhang

2009

IEEE Trans. Neural Netw.

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References

2019

Kinematic Control of Redundant Robot Arms Using Neural Networks

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A time controlling neural network for time‐varying QP solving with application to kinematics of mobile manipulators

et al. 2020

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To obtain the solution for time-varying quadratic programming (QP), a time controlling neural network (TCNN) is presented and discussed. The traditional recurrent neural networks provide a prospect for real-time calculations and repeatable trajectory control of the mobile manipulators due to its high executing processing and nonlinear disposal ability. However, the convergent time is still a considerable point for the solution of a dynamic system dealing with synchronism and robustness. In this note, a TCNN model by incorporating an initial rectified term is applied to solve the online calculation problems and the convergent time can be controlled in advance. Theoretical analyses on stability, prespecified time and convergence are rigorously clarified. Finally, effectiveness and precision of the TCNN model for the solution of a QP example have been verified. In addition, a repetitive trajectory planning for a three-wheel manipulator is introduced to demonstrate the superiority of the TCNN.

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A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations

Cited by 159 publications

References 11 publications

A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

References

A time controlling neural network for time‐varying QP solving with application to kinematics of mobile manipulators

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