Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems

摘要

The globally projected dynamical system has received considerable attention due to its low complexity for variational inequality and optimization computation. This paper obtains further results on the global convergence, asymptotic stability, and exponential stability of this system, respectively under monotonicity of the mapping, strict monotonicity of the mapping, and positive definiteness of the Jacobian matrix of the mapping. The new results obtained improve existing ones and cover the classical stability results of autonomous dynamical systems as special cases. An application to constrained optimization and complementarity problems is given to show the applied significance of the results obtained.