Global exponential stability of a neural network for inverse variational inequalities. (English) Zbl 07403127
Summary: We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions, we establish the exponential stability of the proposed neural network. A discrete version of the proposed neural network is considered, leading to a new projection method for solving inverse variational inequalities, for which we obtain the linear convergence. We illustrate the effectiveness of the proposed neural network and its explicit discretization by considering applications in the road pricing problem arising in transportation science. The results obtained in this paper provide a positive answer to a recent open question and improve several recent results in the literature.
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 49J40 | Variational inequalities |
| 65P40 | Numerical nonlinear stabilities in dynamical systems |
Keywords:
dynamic programming; variational inequality; neural network; exponential stability; road pricing problemReferences:
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