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71.
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
72.
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
73.
Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces 总被引:3,自引:0,他引:3
We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest. 相似文献
74.
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
75.
In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques. 相似文献
76.
汪巍 《数学的实践与认识》2004,34(3):103-109
首先引入了差分系统基于两种度量的极端稳定性概念 ,然后建立了一些关于差分系统 ( h0 ,h)极端稳定性 (极端一致稳定性 ,极端渐近稳定性 ,极端一致渐近稳定性 )的判定准则 .在所得到的定理中 ,对△ V的限制较弱 ,特别地 ,△V甚至可以恒为正 ,从而便于实际应用 . 相似文献
77.
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
78.
Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
79.
Yiran He 《Journal of Global Optimization》2007,39(3):419-426
The existence of global error bound for convex inclusion problems is discussed in this paper, including pointwise global error
bound and uniform global error bound. The existence of uniform global error bound has been carefully studied in Burke and
Tseng (SIAM J. Optim. 6(2), 265–282, 1996) which unifies and extends many existing results. Our results on the uniform global
error bound (see Theorem 3.2) generalize Theorem 9 in Burke and Tseng (1996) by weakening the constraint qualification and
by widening the varying range of the parameter. As an application, the existence of global error bound for convex multifunctions
is also discussed. 相似文献
80.
In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples. 相似文献