On the stability of globally projected dynamical systems

被引:181
作者
Xia, YS [1 ]
Wang, J [1 ]
机构
[1] Chinese Univ Hong Kong, Dept Mech & Automat Engn, Shatin, Hong Kong, Peoples R China
关键词
projected dynamical systems; variational inequalities; stability theory;
D O I
10.1023/A:1004611224835
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
Two types of projected dynamical systems, whose equilibrium states solve the corresponding variational inequality problems, were proposed recently by Dupuis and Nagurney (Ref. 1) and by Friesz et al. (Ref. 2). The stability of the dynamical system developed by Dupuis and Nagurney has been studied completely (Ref. 3). This paper analyzes and proves the global asymptotic stability of the dynamical system proposed by Friesz et al. under monotone and symmetric mapping conditions. Furthermore, the dynamical system is shown to be globally exponentially stable under stronger conditions. Finally, we show that the dynamical system proposed by Friesz et al. can be applied easily to neural networks for solving a class of optimization problems.
引用
收藏
页码:129 / 150
页数:22
相关论文
共 14 条
[1]  
DUPUIS P, 1993, ANN OPER RES, V44, P19, DOI DOI 10.1007/BF02073589
[2]   A CONTINUOUS APPROACH TO OLIGOPOLISTIC MARKET EQUILIBRIUM [J].
FLAM, SD ;
BENISRAEL, A .
OPERATIONS RESEARCH, 1990, 38 (06) :1045-1051
[3]   Dynamic systems, variational inequalities and control theoretic models for predicting time-varying urban network flows [J].
Friesz, TL ;
Bernstein, D ;
Stough, R .
TRANSPORTATION SCIENCE, 1996, 30 (01) :14-31
[4]   DAY-TO-DAY DYNAMIC NETWORK DISEQUILIBRIA AND IDEALIZED TRAVELER INFORMATION-SYSTEMS [J].
FRIESZ, TL ;
BERNSTEIN, D ;
MEHTA, NJ ;
TOBIN, RL ;
GANJALIZADEH, S .
OPERATIONS RESEARCH, 1994, 42 (06) :1120-1136
[5]  
HOPFIELD JJ, 1985, BIOL CYBERN, V52, P141
[6]   NEURAL NETWORKS FOR NONLINEAR-PROGRAMMING [J].
KENNEDY, MP ;
CHUA, LO .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (05) :554-562
[7]  
Khalil H. K., 1996, NONLINEAR SYSTEMS
[8]  
Kinderlehrer D., 1980, An Introduction to Variational Inequalities and Their Applications
[9]  
Ortega JM., 1970, ITERATIVE SOLUTION N
[10]  
SMITH TE, 1995, COMP ANAL 2 MINIMUM, P405