Abstract
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.
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Acknowledgements
The authors are very thankful to both anonymous referees for their careful reading and constructive comments, which helped to improve the presentation of the paper. This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) project 101.01-2019.320. The second author acknowledges the support of the U.S. National Science Foundation under Grant CMMI-2047793.
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Communicated by Alfredo N. Iusem.
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Vuong, P.T., He, X. & Thong, D.V. Global Exponential Stability of a Neural Network for Inverse Variational Inequalities. J Optim Theory Appl 190, 915–930 (2021). https://doi.org/10.1007/s10957-021-01915-x
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DOI: https://doi.org/10.1007/s10957-021-01915-x