Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control  

作　　者：Yang Jun Li Shiyong Long Chengnian Guan Xinping 

机构地区：[1]Coll. of Science, Yanshan Univ.,Qinhuangdao 066004, P. R. China [2]Mathematics Research Center in Hebei Province, Shijiazhuang 050000, P. R. China [3]School of Electronics and Information Engineering, Beijing Jiaotong Univ., Beijing 100044, P. R. China [4]Inst. of Electrical Engineering, Yanshan Univ., Qinhuangdao 066004, P. R. China

出　　处：《Journal of Systems Engineering and Electronics》2007年第3期591-597,共7页系统工程与电子技术（英文版）

基　　金：supported in part by the National Outstanding Youth Foundation of P.R.China (60525303);the National Natural Science Foundation of P.R.China(60404022,60604004);the Natural Science Foundation of Hebei Province (102160);the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005);the NS of Education Office in Hebei Province (2004123).

摘　　要：The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.

关 键 词：flow control Newton-Like algorithm convergence global stability OPTIMIZATION Lyapunov function. 

分 类 号：O242.23[理学—计算数学]