Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2131

 Title: Well-Behavior, Well-Posedness and Nonsmooth Analysis Authors: Penot, Jean-Paul Keywords: Asymptotical Well-BehaviorConditioningCritical SequenceError BoundsGageMetrically Well-SetMinimizing SequenceNice BehaviorPalais-Smale ConditionPtak FunctionQuasi-InverseStationary SequenceWell-BehaviorWell-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. URI: http://hdl.handle.net/10525/2131 ISSN: 0204-9805 Appears in Collections: 1998 Volume 12

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