Prox-regular functions in Hilbert spaces

By F. Bernard, Lionel Thibault. 2005

87 citations recorded by the source corpus.

This paper studies the prox-regularity concept for functions in the general context of Hilbert space. In particular, a subdifferential characterization is established as well as several other properties. It is also shown that the Moreau envelopes of such functions are continuously differentiable.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3014f2274903434af427b4629e613fc78fe46634

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In Computational Theory and Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Second-order growth, tilt stability, and metric regularity of the subdifferential (2013, background): “It is well known from [3, 4, 24, 26] that the class of prox-regular and subdifferentially continuous functions is rather broad including, in particular, strongly amenable functions [26] on IR and all the l.”
Differential properties of the Moreau envelope (2014, methodology): “This property has been extended to Hilbert spaces in [6] by F.”
Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties (2011, background): “Concerning related concepts for functions, we refer to [5, 6, 7, 8, 21, 33, 37, 38, 40, 44] and the references therein, and concerning the other similar concept of subsmoothness for sets, we refer to [2].”
Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces (2006, background): “The proof now is similar to that of [3] or [4].”
Prox-Regularity of Functions and Sets in Banach Spaces (2004, methodology): “functions are ∂-prox-regular: again, the proof is the same as in [27] or [ 2 ].”