ISSN:
1436-4646
Keywords:
Implicit function
;
stationary point
;
strong stability
;
Lipschitz continuity
;
generalized Jacobian
;
mapping degree
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We consider the spaceL(D) consisting of Lipschitz continuous mappings fromD to the Euclideann-space ℝ n ,D being an open bounded subset of ℝ n . LetF belong toL(D) and suppose that $$\bar x$$ solves the equationF(x) = 0. In case that the generalized Jacobian ofF at $$\bar x$$ is nonsingular (in the sense of Clarke, 1983), we show that forG nearF (with respect to a natural norm) the systemG(x) = 0 has a unique solution, sayx(G), in a neighborhood of $$\bar x$$ Moreover, the mapping which sendsG tox(G) is shown to be Lipschitz continuous. The latter result is connected with the sensitivity of strongly stable stationary points in the sense of Kojima (1980); here, the linear independence constraint qualification is assumed to be satisfied.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01588782
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