The Global Exponential Stability of a Dynamical System for Solving Variational Inequalities
- 34 Downloads
We revisit a dynamical system for solving variational inequalities. Under strongly pseudomonotone and Lipschitz continuous assumptions of the considered operator, we obtain the global exponential stability of the trajectories. Numerical examples are presented confirming the theoretical results. The stability result obtained in this paper improves and complements some recent works.
KeywordsGlobal exponential stability Dynamical system Strong pseudomonotonicity Variational inequality
We thank the Editor-in-Chief, Professor Terry L. Friesz and two anonymous referees for their useful comments. This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) grant 101.01-2017.315.
- Facchinei F, Pang SS (2003) Finite-dimensional variational inequalities and complementarity problems, vol I, II. Springer, New YorkGoogle Scholar
- Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:141–152Google Scholar
- Hu X, Wang J (2006) Global stability of a recurrent neural network for solving pseudomonotone variational inequalities. In: Proceedings IEEE International Symp. Circuits Syst., Island of Kos, Greece, pp 755–758Google Scholar
- Kinderlehrer D, Stampcchia G (1980) An introduction to variational inequalities and their applications. Academic, New YorkGoogle Scholar
- Konnov I (2007) Equilibrium models and variational inequalities. Elsevier, AmsterdamGoogle Scholar
- Kosko B (1992) Neural networks for signal processing. Prentice-Hall, Englewood CliffsGoogle Scholar
- Yoshikawa T (1990) Foundations of robotics: analysis and control. MIT Press, CambridgeGoogle Scholar