Recurrent neural networks for solving second-order cone programs

Ko, Chun-Hsu; Chen, Jein Shan; Yang, Chii Rong

doi:10.1016/j.neucom.2011.07.009

Cited by 36 publications

(47 citation statements)

References 23 publications

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“…Moreover, from Lemma 9 and the same argument as in [14,26], the neural network (47) has finite convergence time.…”

Section: Theorem 11 Let * Is the Equilibrium Point Of Neural Networkmentioning

confidence: 83%

“…Its Lyapunov stability and global convergence are proved under some conditions. Finally, we test the projection neural network by some numerical examples and the optimal grasping manipulation problems for multifingered robots and also compare the neural network with the second neural network for some secondorder cone programming problems in paper [14]. Simulation results demonstrate the effectiveness of the proposed neural network.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 97%

“…One type is the smooth neural network, including the merit function method derived from the Fischer-Burmeister function [14], the smoothed natural residual merit function method [15], and the merit function method based on the generalized Fischer-Burmeister function [16]. The other is the projection neural network by replacing the scalar projection function with the cone projection function [14,17]. In paper [18], professor He proposed a neural network based on the simple projection and contraction technique for linear asymmetric variational inequalities.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…In paper [14], two neural networks are proposed for the second-order cone programs. The first neural network uses the Fischer-Burmeister function to achieve an unconstrained minimization with a merit function.…”

Section: Simulation Experimentsmentioning

confidence: 99%

“…The second neural network is a projection neural network. Here we compared our projection neural network method with the neural network based on the cone projection function in paper [14] by the next two test examples.…”

Section: Simulation Experimentsmentioning

confidence: 99%

See 4 more Smart Citations

A Projection Neural Network for Circular Cone Programming

Zhang

Liu

2018

Mathematical Problems in Engineering

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A projection neural network method for circular cone programming is proposed. In the KKT condition for the circular cone programming, the complementary slack equation is transformed into an equivalent projection equation. The energy function is constructed by the distance function and the dynamic differential equation is given by the descent direction of the energy function. Since the projection on the circular cone is simple and costs less computation time, the proposed neural network requires less state variables and leads to low complexity. We prove that the proposed neural network is stable in the sense of Lyapunov and globally convergent. The simulation experiments show our method is efficient and effective.

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“…Moreover, from Lemma 9 and the same argument as in [14,26], the neural network (47) has finite convergence time.…”

Section: Theorem 11 Let * Is the Equilibrium Point Of Neural Networkmentioning

confidence: 83%

Section: Mathematical Problems In Engineeringmentioning

confidence: 97%