Discrete-time projection neural network methods for computing the solution of variational inequalities

Volume 10, Issue 4, pp 1896--1907 http://dx.doi.org/10.22436/jnsa.010.04.49

Publication Date: April 20, 2017 Submission Date: September 05, 2016

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Authors

Liping Zhang - School of Science, Sichuan University of Science and Engineering, Zigong 643000, China. Shu-Lin Wu - School of Science, Sichuan University of Science and Engineering, Zigong 643000, China.

Abstract

Neural networks are useful tools to solve mathematical and engineering problems. By using the implicit-explicit-method and the method proposed recently by Mohamad to discretize the continuous-time neural networks, we formulate two classes of discrete-time analogues to solve a system of variational inequalities. By adopting suitable Lyapunov functions and Razumikhintype techniques, exponential stability of the discrete neural networks are established in terms of linear matrix inequalities (LMIs). Several numerical experiments are performed to compare the convergence rates of the proposed discrete neural networks and it is shown that: (a) all of the discrete neural networks converge faster as the step size becomes larger, (b) the discrete neural networks derived by the semi-implicit Euler method performs best.

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Keywords

• Neural networks
• linear matrix inequalities (LMIs)
• variational inequalities
• discretization.

MSC

•  34K45
•  39A11
•  92B20

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