A new class of generalized f-projected dynamical system in Banach spaces

Abstract

In this article, a new class of generalized f-projected dynamical systems is introduced and studied in Banach spaces. A global existence and uniqueness result of generalized f-projected dynamical system is proved, which generalizes the existence result of Xia and Vincent [Y.S. Xia and T.L. Vincent, On the stability of global projected dynamical systems, J. Optim. Theory Appl. 106 (2009), pp. 129–150]. The global convergence stability of the generalized f-projected dynamical system and the sensitivity result of solutions set with perturbations of the constraint sets are also obtained under some suitable conditions.

Keywords:

• generalized f-projected dynamical system
• convexity modulus
• equilibrium point
• global convergence stability

AMS Subject Classifications::

• 47H05
• 47H09
• 47H10
• 49J40

Acknowledgements

The authors appreciate greatly the editor and two anonymous referees for their useful comments and suggestions, which helped to improve an early version of this article.

This work was supported by the Key Program of NSFC (Grant No. 70831005), the National Natural Science Foundation of China (11171237, 11101069) and the Sichuan University Foundation (SKG 201008).