On error bounds for lower semicontinuous functions

Wu, Zili; Ye, Jane J.

doi:10.1007/s101070100278

Cited by 95 publications

(43 citation statements)

References 9 publications

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“…The above result is obtained in [26] (Th. 8) (expressed in a different way), under the additional assumption that X is reflexive.…”

Section: Theorem 32 Let X Be a Banach Space F : X → R ∪ {+∞} Be A supporting

confidence: 54%

“…3.5)), which was sufficient (and used) for the main purposes of [4], as described in the title of that paper. Since then, the conclusions of Theorem 3.1 have been obtained in [26] (Th. 7), where they are expressed in a more customary way, through the equivalence of several properties.…”

Section: Remark 32 (A)mentioning

confidence: 89%

“…While the proof given in [26] is rather involved, it is easy to see that this can be established in a straightforward way, arguing similarly as in Proposition 2.3 and in Theorem 2.1, but using (the stronger) Proposition 2.2 instead of Corollary 2.…”

Section: Characterization Of Global Error Boundsmentioning

confidence: 99%

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Characterizations of error bounds for lower semicontinuous functions on metric spaces

2004

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Abstract.Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.Mathematics Subject Classification. 49J52, 90C26, 90C25, 49J53.

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“…The above result is obtained in [26] (Th. 8) (expressed in a different way), under the additional assumption that X is reflexive.…”

Section: Theorem 32 Let X Be a Banach Space F : X → R ∪ {+∞} Be A supporting

confidence: 54%

Section: Remark 32 (A)mentioning

confidence: 89%

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Characterizations of error bounds for lower semicontinuous functions on metric spaces

2004

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“…It is strongly related to metric regularity properties. A large number of conditions and characterizations can be found in [2,3,8,9,13,15,16].…”

Section: Error Estimates Under An Hoffman Hypothesismentioning

confidence: 99%

A regularization method for ill-posed bilevel optimization problems

Bergounioux

Haddou

2006

RAIRO-Oper. Res.

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“…The metric regularity of implicit multifunctions has been extensively studied by several authors (see, for example, [2], [5], [8], [25], [24], [39], [46], [56] and the references given therein). Almost all implicit multifunction results in the literature are based on conditions on some tangent cones or on some normal cones to the graphs of the multifunctions involved.…”

Section: Introductionmentioning

confidence: 99%

Implicit multifunction theorems in complete metric spaces

2013

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In this paper, we establish some new characterizations of the metric regularity of implicit multifunctions in complete metric spaces by using the lower semicontinuous envelopes of the distance functions for set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.Mathematics Subject Classification: 49J52, 49J53, 90C30.

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On error bounds for lower semicontinuous functions

Cited by 95 publications

References 9 publications

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Characterizations of error bounds for lower semicontinuous functions on metric spaces

A regularization method for ill-posed bilevel optimization problems

Implicit multifunction theorems in complete metric spaces

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