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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Further Results on the Stability of Neural Network for Solving Variational Inequalities

Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 341--353 | DOI:10.5890/DNC.2016.12.001

Mi Zhou$^{1}$, Xiaolan Liu$^{2}$,$^{3}$

1School of Science and Technology, Sanya College, Sanya, Hainan 572022, China

2College of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

3Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong, Sichuan 643000, China

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This paper analyzes and proves the global Lyapunov stability of the neural network proposed by Yashtini and Malek when the mapping is continuously differentiable and the Jacobian matrix of the mapping is positive semi-definite. Furthermore, the neural network is shown to be exponentially stable under stronger conditions. In particular, the stability results can be applied to the stability analysis of variational inequalities with linear constraints and bounded constraints. Some examples show that the proposed neural network can be used to solve the various nonlinear optimization problems. The new results improve the existing ones in the literature.


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