LIPSCHITZIAN INVERSE FUNCTIONS, DIRECTIONAL-DERIVATIVES, AND APPLICATIONS IN C1,1 OPTIMIZATION

被引：36

作者：

KUMMER, B

机构：

[1] Department of Mathematics, Humboldt University Berlin, Berlin

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1991年 / 70卷 / 03期

关键词：

INVERSE LIPSCHITZ FUNCTIONS; IMPLICIT FUNCTIONS; DIRECTIONAL DERIVATIVES; MEAN-VALUE THEOREM; CHAIN RULES; STRONGLY STABLE CRITICAL POINTS;

D O I：

10.1007/BF00941302

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：

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable in C1,1 optimization problems.

引用

页码：561 / 582

页数：22

共 23 条

[1]

AUBIN JP, 1984, APPLIED NONLINEAR AN

[2]

Clarke F.H., 1983, OPTIMIZATION NONSMOO

[3] INVERSE FUNCTION THEOREM [J].

CLARKE, FH .

PACIFIC JOURNAL OF MATHEMATICS, 1976, 64 (01) :97-102

[4]

Dem'yanov V.F., 1986, QUASIDIFFERENTIAL CA

[5]

Hiriart-Urruty J. B., 1979, Mathematics of Operations Research, V4, P79, DOI 10.1287/moor.4.1.79

[6] GENERALIZED HESSIAN MATRIX AND 2ND-ORDER OPTIMALITY CONDITIONS FOR PROBLEMS WITH C1,1 DATA [J].

HIRIARTURRUTY, JB ;

STRODIOT, JJ ;

NGUYEN, VH .

APPLIED MATHEMATICS AND OPTIMIZATION, 1984, 11 (01) :43-56

[7]

HIRIARTURRUTY JB, 1982, MATH PROGRAM STUD, V17, P1

[8]

JONGEN HT, 1988, TH1 AACH PREPR

[9]

KLATTE B, 1988, ADV MATH OPTIMIZATIO, P104

[10]

Klatte D., 1988, Optimization, V19, P169, DOI 10.1080/02331938808843333

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