共查询到20条相似文献,搜索用时 46 毫秒
1.
Phil Diamond Peter Kloeden Alexander Rubinov Alexander Vladimirov 《Set-Valued Analysis》1997,5(3):267-289
Along with the Hausdorff metric, we consider two other metrics on the space of convex sets, namely, the metric induced by the Demyanov difference of convex sets and the Bartels–Pallaschke metric. We describe the hierarchy of these three metrics and of the corresponding norms in the space of differences of sublinear functions. The completeness of corresponding metric spaces is demonstrated. Conditions of differentiability of convex-valued maps of one variable with respect to these metrics are proved for some special cases. Applications to the theory of convex fuzzy sets are given. 相似文献
2.
We investigate some geometric properties of level sets of the solutions of parabolic problems in convex rings. We introduce the notion of parabolic quasi‐concavity, which involves time and space jointly and is a stronger property than the spatial quasi‐concavity, and study the convexity of superlevel sets of the solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上.打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理. 相似文献
4.
Richard A. Vitale 《Set-Valued Analysis》1993,1(1):89-96
We extend to infinite dimensions a class of bounds forL
p metrics of finite-dimensional convex bodies. A generalization to arbitrary increasing convex functions is done simultaneously. The main tool is the use of Gaussian measure to effect a normalization for varying dimension. At a point in the proof we also invoke a strong law of large numbers for random sets to produce a rotational averaging.Supported in part by ONR Grant N0014-90-J-1641 and NSF Grant DMS-9002665. 相似文献
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We introduce in this work some normed space notions such as norming, thin and thick sets in general locally convex spaces. We also study some effects of thick sets on the uniform boundedness-like principles in locally convex spaces such as “weak*-bounded sets are strong*-bounded if and only if the space is a Banach–Mackey space”. It is proved that these principles occur under some weaker conditions by means of thick sets. Further, we show that the thickness is a duality invariant, that is, all compatible topologies for some locally convex space have the same thick sets. 相似文献
7.
M. A. Sevodin 《Russian Mathematics (Iz VUZ)》2013,57(10):62-64
We consider sets which are convex in directions from some cone K. We generalize some well-known properties of ordinary convex sets for the case of K-convex sets and give some applications in optimization theory. 相似文献
8.
For an inequality constrained nonsmooth multiobjective optimization problem involving locally Lipschitz functions, stronger KT-type necessary conditions and KT necessary conditions (which in the continuously differentiable case reduce respectively to the stronger KT conditions studied recently by Maeda and the usual KT conditions) are derived for efficiency and weak efficiency under several constraint qualifications. Stimulated by the stronger KT-type conditions, the notion of core of the convex hull of the union of finitely many convex sets is introduced. As main tool in the derivation of the necessary conditions, a theorem of the alternatives and a core separation theorem are also developed which are respectively extensions of the Motzkin transposition theorem and the Tucker theorem. 相似文献
9.
本文证明了由Zonoid体生成的凸柱体的一个极值性质,并研究了在John基上的凸摄动体的最大Hausodorff距离和平均宽度的下界. 相似文献
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V. F. Babenko 《Ukrainian Mathematical Journal》1992,44(5):519-528
This paper is devoted to an exact solution of problems of best approximation in the uniform and integral metrics of classes of periodic functions representable as a convolution of a kernel not increasing the oscillation with functions having a given convex upwards majorant of the modulus of continuity. The approximating sets are taken to be the trigonometric polynomials in the case of the uniform and integral metrics, and convolutions of the kernel defining the class with polynomial splines in the case of the integral metric.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 579–589, May, 1992. 相似文献
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The notion of convex cones in general position has turned out to be useful in convex programming theory. In this paper we extend the notion to convex sets and give some characterizations which yield a better insight into this concept. We also consider the case of convex sets in S-general position. 相似文献
14.
M. Zähle 《Geometriae Dedicata》1999,76(2):183-187
For integral geometric and local topological properties of two sets of positive reach, one fixed and the other moving or translating, certain exceptional relative positions have to be excluded. We give a measure geometric justification in form of a Sard-type theorem which extends to more general singular sets. A slightly stronger result has been proved by Schneider for the special case of convex bodies. 相似文献
15.
Jean-Paul Penot 《Proceedings of the American Mathematical Society》2003,131(8):2371-2377
We present fixed point theorems for a nonexpansive mapping from a closed convex subset of a uniformly convex Banach space into itself under some asymptotic contraction assumptions. They generalize results valid for bounded convex sets or asymptotically compact sets.
16.
First-order criteria for pseudomonotonicity and quasimonotonicity are given for differentiable maps on open convex sets. These
criteria are proved stronger than those introduced earlier.
This research was supported by the National Research Council of Canada, Grant No A8312. 相似文献
17.
August Florian 《Geometriae Dedicata》1989,30(1):69-80
A distance function, defined in [12], for the class of compact convex sets inn-space is introduced in a new way, and some of its properties are developed. This concept is compared with some traditional
distance functions for convex sets. 相似文献
18.
In this article, we deal with some computational aspects of geodesic convex sets. Motzkin-type theorem, Radon-type theorem, and Helly-type theorem for geodesic convex sets are shown. In particular, given a finite collection of geodesic convex sets in a simple polygon and an “oracle,” which accepts as input three sets of the collection and which gives as its output an intersection point or reports its nonexistence; we present an algorithm for finding an intersection point of this collection. 相似文献
19.
F. Glover 《Mathematical Methods of Operations Research》1974,18(5):181-186
This note shows that convexity cuts defined relative to polyhedral convex sets can utilize negative as well as positive edge extensions under appropriate circumstances, yielding stronger cuts than customarily available. We also show how to partially collapse the polyhedron to further improve these cuts. 相似文献
20.
Truong Xuan Duc Ha 《Optimization》2019,68(7):1321-1335
AbstractThis short paper characterizes strictly convex sets by the uniqueness of support points (such points are called unique support points or exposed points) under appropriate assumptions. A class of so-called regular sets, for which every extreme point is a unique support point, is introduced. Closed strictly convex sets and their intersections with some other sets are shown to belong to this class. The obtained characterizations are then applied to set-valued maps and to the separation of a convex set and a strictly convex set. Under suitable assumptions, so-called set-valued maps with path property are characterized by strictly convex images of the considered set-valued map. 相似文献