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1.
关于Banach空间中凸泛函的广义次梯度不等式 总被引:2,自引:0,他引:2
本文在前人^[1,2]的基础之上,以凸泛函的次梯度不等式为工具,将Jensen不等式推广到Banach空间中的凸泛函,导出了Banach空间中的Bochner积分型的广义Jensen不等式,给出其在Banach空间概率论中某些应用,从而推广了文献[3—6]的工作. 相似文献
2.
Lahcne Mezrag 《Mathematische Nachrichten》2004,266(1):60-67
In [5], it is proved that a bounded linear operator u, from a Banach space Y into an Lp(S, ν) factors through Lp1 (S, ν) for some p1 > 1, if Y* is of finite cotype; (S, ν) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uv, where u : Y → Lp(S, ν) and v : X → Y are linear operators such that v* is of finite Ka?in cotype. This result gives also a new proof of Grothendieck's theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Xu Tianzhou 《东北数学》1997,(1)
ModulesoverOperatorAlgebrasandItsModuleMapsXuTianzhou(许天周)(DepartmentofMathematics,NanjingUniersity,Nanjing,210093)AbstractLe... 相似文献
4.
Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union
of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of
verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which
can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key
roles in solving large scale knowledge-based data classification problems where they are used to describe the containments
as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which
was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments. 相似文献
5.
M.Z. Arslanov 《Operations Research Letters》2007,35(5):636-644
We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem. 相似文献
6.
We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Jonathan M. Borwein 《Optimization Letters》2007,1(1):21-32
This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex. 相似文献
8.
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional
random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise
symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable
pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is
treated by a variation of Stein’s method which is adapted for continuous symmetries.
This work was done while at Stanford University. 相似文献
9.
C. Bogani M. G. Gasparo A. Papini 《Journal of Optimization Theory and Applications》2007,134(1):47-59
We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search
methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that
it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to
ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical
experiments seem to be encouraging.
This work was supported by M.U.R.S.T., Rome, Italy. 相似文献
10.
M. Pappalardo 《Journal of Optimization Theory and Applications》1991,70(1):97-107
We prove a property of the Bouligand tangent cone to the epigraph (or to the graph) of a locally Lipschitz function. It is also shown how this result can be used in determining Dini sequences. Finally, some relationships between such a cone and Dini derivatives are provided. 相似文献