Metric projections and the differentiability of distance functions
نویسندگان
چکیده
منابع مشابه
Local Differentiability of Distance Functions
Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets C for which the distance function dC is continuously differentiable everywhere on an open “tube” of uniform thickness around C. Here a corresponding local theory is developed for the property of dC being continuously differentiable outside of C on some neighborhood of a point x ∈ C. This is shown to be equ...
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This paper considers metric projections onto a closed subset S of a Hilbert space. If the set S is convex, then it is well known that the corresponding metric projections always exist, unique and directionally differentiable at boundary points of S. These properties of metric projections are considered for possibly nonconvex sets S. In particular, existence and directional differentiability of ...
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We consider properties of the metric projections onto moving convex sets in normed linear spaces. Under certain conditions about the norm, directional diierentiability (of higher order) of the metric projections at boundary points is characterized. The characterization is formulated in terms diierentiability of multifunctions and properties of the set-derivatives are shown.
متن کاملDifferentiability Properties of Metric Projections onto Convex Sets
It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems.
متن کاملDifferentiability of Distance Functions and a Proximinal Property Inducing Convexity
In a normed linear space X, consider a nonempty closed set K which has the property that for some r > 0 there exists a set of points xo € X\K, d(xoK) > r, which have closest points p(xo) € K and where the set of points xo — r((xo — p(xo))/\\xo — p(zo)||) is dense in X\K. If the norm has sufficiently strong differentiability properties, then the distance function d generated by K has similar dif...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1980
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700006596