Local differentiability of distance functions

By R. Poliquin, R. Tyrrell Rockafellar, Lionel Thibault. 2000

480 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/057db510e753021b7a3c3f864e8fbd3744c20153

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Using a signed distance function for the simulation of metal forming processes: Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach (2009, background): “See [8] for the theoretical aspects about this subject.”
Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems (2010, background): “, [36, 38] for several other examples as well as results of preservation of prox-regularity under operations.”
Differential properties of the Moreau envelope (2014, unknown): “27) is exactly E 1 2 ,X ψS(·) and d2 S(·) is a C1,1 function, see [1,36,49].”
Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties (2011, methodology): “This paper is based on a previous work of ours [9] where we extended in some sense the study made in [39] of prox-regular sets C in Hilbert spaces.”
Approximation and regularization of Lipschitz functions: convergence of the gradients (2006, unknown): “They are called proximally smooth sets by Clarke, Stern and Wolenski [10], prox regular sets by Poliquin and Rockafellar [30], Poliquin, Rockafellar and Thibault [31], and sets with property ρ by Plaskacz [28].”
Prox-Regularity of Functions and Sets in Banach Spaces (2004, unknown): “In the case where f is the indicator function of a closed set C, they are equivalent as proved by Poliquin, Rockafellar and Thibault in [ 28 ] and they translate the prox-regularity of C. Indeed, they mean respectively that the square distance function to C, d 2”
Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces (2006, background): “On the local level, in the study of sets C for which dC is locally differentiable and its consequences for the metric projection mapping PC , Poliquin, Rockafellar and Thibault [39] recently made advance in the Hilbert setting with a different point of view, by making the link with the local propert”
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods (2013, background): “Prominent examples of prox-regular sets are closed convex sets and C2 submanifolds of R (see [50] and references therein).”
Subsmooth sets: Functional characterizations and related concepts (2004, background): “We recall from [25] that the set C is called prox-regular at u0, if for every r > 0, there exists σ, δ > 0 such that for all u1, u2 ∈ B(u0, δ) ∩ C and all ui ∈ N (C; ui), i ∈ {1, 2}, one has”
Sweeping by a continuous prox-regular set $ (2003, background): “, [24], and [5,6,12], where such sets are called j-convex).”
Iterative schemes to solve nonconvex variational problems. (2003, background): “For the proof of these results we refer the reader to [10, 17 ].”
THE DISTANCE FUNCTION FROM THE BOUNDARY IN A MINKOWSKI SPACE (2006, methodology): “We mention, among other papers, [15] in the framework of general first order Hamilton–Jacobi equations and Finsler geometry, [14] and [17] in the case of Riemannian manifolds, [10] and [21] for the point of view of non–smooth analysis in Hilbert spaces, [13] for results applied to the theory of Sobo”