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1998 Volume 12 >

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Title: Well-Behavior, Well-Posedness and Nonsmooth Analysis
Authors: Penot, Jean-Paul
Keywords: Asymptotical Well-Behavior
Critical Sequence
Error Bounds
Metrically Well-Set
Minimizing Sequence
Nice Behavior
Palais-Smale Condition
Ptak Function
Stationary Sequence
Well-Posed Problem
Issue Date: 1998
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Pliska Studia Mathematica Bulgarica, Vol. 12, No 1, (1998), 141p-190p
Abstract: We survey the relationships between well-posedness and well-behavior. The latter notion means that any critical sequence (xn) of a lower semicontinuous function f on a Banach space is minimizing. Here “critical” means that the remoteness of the subdifferential ∂f(xn) of f at xn (i.e. the distance of 0 to ∂f(xn)) converges to 0. The objective function f is not supposed to be convex or smooth and the subdifferential ∂ is not necessarily the usual Fenchel subdifferential. We are thus led to deal with conditions ensuring that a growth property of the subdifferential (or the derivative) of a function implies a growth property of the function itself. Both qualitative questions and quantitative results are considered.
Description: AMS subject classification: 90C30, 90C33.
ISSN: 0204-9805
Appears in Collections:1998 Volume 12

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