Abstract
In this paper, a new neural network for a class of variational inequalities with linear and nonlinear constraints is proposed by converting it into an extended variational inequality. The proposed neural network with the asymmetric mapping is proved to be stable in the sense of Lyapunov and converge to a solution of the original problem within a finite time under a weaker co-coercivity condition by using a convex energy function. Meanwhile, the finite-time convergence for the proposed network with the gradient mapping is also shown under some mild conditions. Compared with the existing neural networks, the new model is suitable to parallel implementation with lower complexity, and can be applied to solve some nonmonotone problems. The validity and transient behavior of the proposed neural network are demonstrated by numerical examples.
This work was supported in part by NSFC Grant of China No. 10571115.
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Gao, XB., Du, LL. (2006). A Neural Network with Finite-Time Convergence for a Class of Variational Inequalities. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_4
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DOI: https://doi.org/10.1007/11816157_4
Publisher Name: Springer, Berlin, Heidelberg
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