Abstract
We investigate the global exponential stability of equilibrium solutions of a projected dynamical system for variational inequalities. Under strong pseudomonotonicity and Lipschitz continuity assumptions, we prove that the dynamical system has a unique equilibrium solution. Moreover, this solution is globally exponentially stable. Some examples are given to analyze the effectiveness of the theoretical results. The numerical results confirm that the trajectory of the dynamical system globally exponentially converges to the unique solution of the considered variational inequality. The results established in this paper improve and extend some recent works.
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Acknowledgements
The authors would like to thank the Editor and the anonymous referee for their useful comments. This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) grant 101.01-2017.315 and the Austrian Science Foundation (FWF), grant P26640-N25. Support provided by the Institute for Computational Science and Technology at Ho Chi Minh City (ICST) is also gratefully acknowledged.
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Ha, N.T.T., Strodiot, J.J. & Vuong, P.T. On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities. Optim Lett 12, 1625–1638 (2018). https://doi.org/10.1007/s11590-018-1230-5
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DOI: https://doi.org/10.1007/s11590-018-1230-5