A novel neurodynamic reaction-diffusion model for solving linear variational inequality problems and its application

Abstract In this paper, we present a new delayed projection neural network with reaction-diffusion terms for solving linear variational inequality problems. The proposed neural network possesses a simple one-layer structure. By employing the differential inequality technique and constructing a new Lyapunov–Krasovskii functional, we derive some novel sufficient conditions ensuring the globally exponential stability. These conditions are dependent on diffusions and the monotonicity assumption is unnecessary. Furthermore, the considered neural network can solve quadratic programming problems. Finally, several applicable examples are provided to illustrate the satisfactory performance of the proposed neural network.

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