Linear Structure of Functions with Maximal Clarke Subdifferential
نویسندگان
چکیده
منابع مشابه
Lipschitz functions with maximal Clarke subdifferentials are staunch
In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.
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The aim of this note is to give an alternative proof for a recent result due to Dorsch, Jongen and Shikhman, which provides an upper estimate for the Clarke subdifferential of an infimal value function. We show the validity of this result under a weaker condition than the one assumed in the mentioned paper, while the use of the Mordukhovich subdifferential, as an intermediate step, will conside...
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In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdiierential mapping of a real-valued locally Lipschitz function is a minimal weak cusco. We then use this characterisation to deduce some new results concerning Lips-chitz functions with minimal subdiierential mappings. In the papers 7] and 1], the authors investigate a class of locally Lipschitz functions ...
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We establish the following result: if the graph of a lower semicontinuous real-extendedvalued function f : Rn → R ∪ {+∞} admits a Whitney stratification (so in particular if f is a semialgebraic function), then the norm of the gradient of f at x ∈ dom f relative to the stratum containing x bounds from below all norms of Clarke subgradients of f at x. As a consequence, we obtain a Morse-Sard typ...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2019
ISSN: 1052-6234,1095-7189
DOI: 10.1137/18m1211398