共查询到20条相似文献,搜索用时 62 毫秒
1.
R.J. Gardner 《Advances in Mathematics》2007,216(1):358-386
This paper develops a significant extension of E. Lutwak's dual Brunn-Minkowski theory, originally applicable only to star-shaped sets, to the class of bounded Borel sets. The focus is on expressions and inequalities involving chord-power integrals, random simplex integrals, and dual affine quermassintegrals. New inequalities obtained include those of isoperimetric and Brunn-Minkowski type. A new generalization of the well-known Busemann intersection inequality is also proved. Particular attention is given to precise equality conditions, which require results stating that a bounded Borel set, almost all of whose sections of a fixed dimension are essentially convex, is itself essentially convex. 相似文献
2.
Partially finite convex programming,Part I: Quasi relative interiors and duality theory 总被引:6,自引:0,他引:6
We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for a fundamental Fenchel duality result, and then deduce duality results for these problems despite the almost invariable failure of the standard Slater condition. Part II of this work studies applications to more concrete models, whose dual problems are often finite-dimensional and computationally tractable. 相似文献
3.
We develop a method for generating valid convex quadratic inequalities for mixed0–1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities. 相似文献
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This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
7.
Sehie Park 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):1028-1042
The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. A KKM space is an abstract convex space satisfying the partial KKM principle and its “open” version. In this paper, we clearly derive a sequence of a dozen statements which characterize the KKM spaces and equivalent formulations of the partial KKM principle. As their applications, we add more than a dozen statements including generalized formulations of von Neumann minimax theorem, von Neumann intersection lemma, the Nash equilibrium theorem, and the Fan type minimax inequalities for any KKM spaces. Consequently, this paper unifies and enlarges previously known several proper examples of such statements for particular types of KKM spaces. 相似文献
8.
《European Journal of Operational Research》2006,169(3):1079-1095
The evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set (hence the convex hull is contained in the evenly convex hull). This paper deals with finite dimensional linear systems containing strict inequalities and (possibly) weak inequalities as well as equalities. The number of inequalities and equalities in these systems is arbitrary (possibly infinite). For such kind of systems a consistency theorem is provided and those strict inequalities (weak inequalities, equalities) which are satisfied for every solution of a given system are characterized. Such results are formulated in terms of the evenly convex hull of certain sets which depend on the coefficients of the system. 相似文献
9.
We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional inequalities are proven for functions whose second derivative in absolute values are convex. Applications of the main results are presented.
相似文献10.
The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many
closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization
(constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard
constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull
intersection property. Jameson’s duality for two cones, which relates bounded linear regularity to property (G), is re-derived
and refined. For polyhedral cones, a statement dual to Hoffman’s error bound result is obtained. A sharpening of a result
on error bounds for convex inequalities by Auslender and Crouzeix is presented. Finally, for two subspaces, property (G) is
quantified by the angle between the subspaces.
Received October 1, 1997 / Revised version received July 21, 1998? Published online June 11, 1999 相似文献
11.
Saad Ihsan Butt Josip Pečarić Ana Vukelić 《Mediterranean Journal of Mathematics》2016,13(4):1495-1511
We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the ?eby?ev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities. 相似文献
12.
关于凸函数的一般平均不等式 总被引:3,自引:1,他引:2
杨镇杭 《数学的实践与认识》2003,33(8):136-141
本文提出并证明了凸函数的最一般的平均不等式 ,是凸函数的幂平均、双参数平均不等式的进一步推广 相似文献
13.
该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式. 相似文献
14.
考察十余种国内通用的高等数学教材对凸函数定义的异同,论证凸函数的两种原始定义之间的关系,给出凸函数所满足的三个重要不等式,并证明凸函数在一元函数微分学范围内所满足的两个重要性质——连续性和单侧可导性。利用实分析中的Hausdorff极大定理给出满足第一种原始定义而不满足第二种原始定义的一个函数的例子. 相似文献
15.
《Optimization》2012,61(4):303-325
This paper studies types of Hausdorff discontinuity from above for point-to-set mappings given with a finite system of convex (in a special case, convex polynomial) inequalities. The discontinuity is with regard to perturbations of the right-side of those inequalities. 相似文献
16.
mdat can 《Numerical Methods for Partial Differential Equations》2021,37(1):118-130
In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results presented here would provide extensions of those given in earlier works. 相似文献
17.
我们根据一般化凸空间上的KKM型定理得到了截口定理,然后作为它的应用讨论了若干个择一不等式.最后,引进了一个具体的一般化凸空间并在该空间上讨论了择一不等式解的存在性问题. 相似文献
18.
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
19.
H. Groemer 《Geometriae Dedicata》1990,33(1):117-122
Using a recently established stability result regarding the Brunn-Minkowski theorem and simple facts about convex functions we find strengthened versions of known inequalities for the mixed volumes of convex bodies. These results improve previously known inequalities of this type.Supported by National Science Foundation Research Grant DMS 870189. 相似文献
20.
We consider the linear programming formulation of the asymmetric travelling salesman problem. Several new inequalities are stated which yield a sharper characterization in terms of linear inequalities of the travelling salesman polytope, i.e., the convex hull of tours. In fact, some of the new inequalities as well as some of the well-known subtour elimination constraints are indeed facets of the travelling salesman polytope, i.e., belong to the class of inequalities that uniquely characterize the convex hull of tours to an-city problem. 相似文献