Neural network with added inertia for linear complementarity problem

In this brief, considering the inertial term into first order neural networks(NNs), an inertial NN(INN) modeled by means of a differential inclusion is proposed for solving linear complementarity problem with $P_{0}$ matrix. Compared with existing NNs, the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different optimal solution. It is proved that the proposed NN is stable in the sense of Lyapunov and any equilibrium of our NN is the optimal solution of LCP with $P_{0}$ matrix. Simulation results on two numerical examples show the effectiveness and performance of the proposed neural network.

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