منابع مشابه
Sweeping process by prox-regular sets in Riemannian Hilbert manifolds
— In this paper, we deal with sweeping processes on (possibly infinitedimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of th...
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We study the convergence of an iterative projection/reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics. There are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem: nonconvexity and infeasibility. The algorithm that we developed, called Relaxed Averaged Alternating Reflections (RAAR), was ...
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The geost constraint has been proposed to model and solve discrete placement problems involving multi-dimensional boxes (packing in space and time). The filtering technique is based on a sweeping algorithm that requires the ability for each constraint to compute a forbidden box around a given fixed point and within a surrounding area. Several cases have been studied so far, including integer li...
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Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2 functions. The class of prox-regular functions covers all convex functions, lower C2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...
متن کاملSweeping out on a Set of Integers
Let (X, ®, m) be a Lebesgue space, m(X) = 1, and let T be an invertible measurable nonsingular aperiodic transformation of X onto X. If S is a set of r integers, r > 2, then there exists a set A of measure less than /•"' S*_! k~l such that X = U,es T"A. Thus for every infinite set of integers W there exist sets A of arbitrarily small measure such that X = U nniv T"A.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2003
ISSN: 0022-0396
DOI: 10.1016/s0022-0396(02)00021-9