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Optimization Letters

, Volume 12, Issue 7, pp 1625–1638 | Cite as

On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities

  • Nguyen Thi Thu Ha
  • J. J. StrodiotEmail author
  • Phan Tu Vuong
Original Paper

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.

Keywords

Global exponential stability Projected dynamical system Strong pseudomonotonicity Variational inequality 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ho Chi Minh City University of Technology and EducationThu Duc, Ho Chi Minh CityVietnam
  2. 2.University of NamurNamurBelgium
  3. 3.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

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