AN INVERSE MAPPING-THEOREM FOR SET-VALUED MAPS

被引:106
作者
DONTCHEV, AL [1 ]
HAGER, WW [1 ]
机构
[1] UNIV FLORIDA,DEPT MATH,GAINESVILLE,FL 32611
关键词
SET-VALUED MAP; INVERSE FUNCTION; PSEUDO-LIPSCHITZ MAP; LIPSCHITZ SELECTION;
D O I
10.2307/2160425
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f + F)-1 when f has vanishing strict derivative.
引用
收藏
页码:481 / 489
页数:9
相关论文
共 23 条
[1]  
Aubin J.P., 1990, SET-VALUED ANAL, V2, DOI 10.1007/978-0-8176-4848-0
[2]   LIPSCHITZ BEHAVIOR OF SOLUTIONS TO CONVEX MINIMIZATION PROBLEMS [J].
AUBIN, JP .
MATHEMATICS OF OPERATIONS RESEARCH, 1984, 9 (01) :87-111
[3]   STABILITY AND REGULAR POINTS OF INEQUALITY SYSTEMS [J].
BORWEIN, JM .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1986, 48 (01) :9-52
[4]   VERIFIABLE NECESSARY AND SUFFICIENT CONDITIONS FOR OPENNESS AND REGULARITY OF SET-VALUED AND SINGLE-VALUED MAPS [J].
BORWEIN, JM ;
ZHUANG, DM .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 134 (02) :441-459
[5]  
Clarke F.H., 1983, OPTIMIZATION NONSMOO
[6]   LIPSCHITZIAN STABILITY IN NONLINEAR CONTROL AND OPTIMIZATION [J].
DONTCHEV, AL ;
HAGER, WW .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1993, 31 (03) :569-603
[7]  
DONTCHEV AL, IN PRESS MATH OPER R
[8]   SOME MAPPING THEOREMS [J].
GRAVES, LM .
DUKE MATHEMATICAL JOURNAL, 1950, 17 (02) :111-114
[10]  
IOFFE AD, 1979, REGULAR POINTS LIPSC