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1.
For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.
Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall
into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation.
For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal
convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games
that generalise the marginalistic interpretation of convexity.
Received: December 2000 相似文献
2.
为研究度量线性空间中凸集的逼近性质,G.C.Ahuja等引起了度量线性空间的严格凸性及一致凸性的定义。本文证明了完备的一致凸的度量线性空间是自反的。同时,作为应用,研究了最佳联合逼近元的存在性与唯一性问题。 相似文献
3.
In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these
sets are core elements, then the game is convex. This approach leads to new upperbounds on the number of marginal vectors
needed to characterize convexity. Another result is that the relative number of marginals needed to characterize convexity
converges to zero.
Received: May 2002 相似文献
4.
Summary The problem of computing constrained spline functions, both for ideal data and noisy data, is considered. Two types of constriints are treated, namely convexity and convexity together with monotonity. A characterization result for constrained smoothing splines is derived. Based on this result a Newton-type algorithm is defined for computing the constrained spline function. Thereby it is possible to apply the constraints over a whole interval rather than at a discrete set of points. Results from numerical experiments are included. 相似文献
5.
Summary.
We consider convex interpolation with
cubic splines on
grids built by adding two knots in each subinterval of neighbouring data
sites. The additional knots have to be variable in order to get a chance
to always retain convexity. By means of the staircase algorithm we
provide computable intervals for the added knots such that all knots
from these intervals allow convexity preserving spline interpolation of
continuity.
Received
May 31, 1994 / Revised version received December 22, 1994 相似文献
6.
The paper deals with the semiconvexity properties (i.e., the rank 1 convexity, quasiconvexity, polyconvexity, and convexity)
of rotationally invariant functions f of matrices. For the invariance with respect to the proper orthogonal group and the invariance with respect to the full orthogonal group coincide.
With each invariant f one can associate a fully invariant function of a square matrix of type where It is shown that f has the semi convexity of a given type if and only if has the semiconvexity of that type. Consequently the semiconvex hulls of f can be determined by evaluating the corresponding hulls of and then extending them to matrices by rotational invariance.
Received: 10 October 2001 / Accepted: 23 January 2002 // Published online: 6 August 2002
RID="*"
ID="*" This research was supported by Grant 201/00/1516 of the Czech Republic. 相似文献
7.
Janusz Matkowski 《Aequationes Mathematicae》1992,43(1):106-112
Summary Leta (0, 1/2] be fixed. A functionf satisfying the inequalityf(ax + (1 – a)y) + f((1 – a)x + ay) f(x) + f(y), called herea-Wright convexity, appears in connection with the converse of Minkowski's inequality. We prove that every lower semicontinuousa-Wright convex function is Jensen convex and we pose an open problem. Moreover, using the fact that 1/2-Wright convexity coincides with Jensen convexity, we prove a converse of Minkowski's inequality without any regularity conditions. 相似文献
8.
M.S. Moslehian 《Linear algebra and its applications》2009,430(4):1131-1987
We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 相似文献
9.
Pham Huu Sach 《Numerical Functional Analysis & Optimization》2013,34(3-4):341-351
We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot . A detailed discussion is devoted to special cases when the contingent, the Fréchet and the Clarke-Rockafellar subdifFerentials Sixe used as this abstract subdifferential. 相似文献
10.
We show existence and uniqueness of the equivariant isometric immersions of Riemannian surfaces into Lorentz space-forms
under conditions implying convexity, when we impose that the associated representations leave a point invariant.
Received: 2 December 1995 相似文献
11.
Tin-Yau Tam 《Linear and Multilinear Algebra》1997,43(1):87-113
The relationship between the classical Schur-Horn's theorem on the diagonal elements of a Hermitian matrix with prescribed eigenvalues and Kostant's convexity theorem in the context of Lie groups. By using Kostant's convexity theorem, we work out the statements on the special orthogonal group and the symplectic group explicitly. Schur-Horn's result can be stated in terms of a set of inequalities. The counterpart in the Lie-theoretic context is related to a partial ordering, introduced by Atiyah and Bott, defined on the closed fundamental Weyl chamber. Some results of Thompson on the diagonal elements of a matrix with prescribed singular values are recovered. Thompson-Poon's theorem on the convex hull of Hermitian matrices with prescribed eigenvalues is also generalized. Then a result of Atiyah-Bott is recovered. 相似文献
12.
Alexander J. Zaslavski 《Calculus of Variations and Partial Differential Equations》2001,13(3):265-293
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands
f which satisfy convexity and growth conditions. In [27] we considered a class of optimal control problems which is identified
with the corresponding complete metric space of integrands, say . We did not impose any convexity assumptions. The main result in [27] establishes that for a generic integrand the corresponding optimal control problem is well-posed. In this paper we study the set of all integrands for which the corresponding optimal control problem is well-posed. We show that the complement of this set is not only of
the first category but also a -porous set. The main result of the paper is obtained as a realization of a variational principle which can be applied to
various classes of optimization problems.
Received April 15, 2000 / Accepted October 10, 2000 / Published online December 8, 2000 相似文献
13.
半模糊凸模糊映射 总被引:1,自引:1,他引:0
In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity. 相似文献
14.
Wiesław Kubiś 《Journal of Geometry》2002,74(1-2):110-119
The purpose of this paper is to investigate some separation properties of sets with axiomatically defined convexity structures.
We state a general separation theorem for pairs of convexities, improving some known results. As an application, we discuss
separation properties of lattices, real vector spaces and modules.
Received 21 January 1999. 相似文献
15.
Admissible slopes for monotone and convex interpolation 总被引:1,自引:0,他引:1
Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC
1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C
1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions. 相似文献
16.
In the general first-level classification of the
convexity properties for sets, discrete convexities appear
in more
classes. A second-level classification identifies more subclasses containing
discrete convexity properties, which appear as approximations either of classical convexity or of fuzzy convexity.
First, we prove that all these convexity concepts are defined by segmental methods. The type
of segmental method involved in the construction of discrete convexity
determines the subclass to which it belongs. The subclasses containing the
convexity properties that have discrete particular cases are also presented. 相似文献
17.
Tin-Yau Tam 《Linear and Multilinear Algebra》2013,61(1-3):87-113
The relationship between the classical Schur-Horn's theorem on the diagonal elements of a Hermitian matrix with prescribed eigenvalues and Kostant's convexity theorem in the context of Lie groups. By using Kostant's convexity theorem, we work out the statements on the special orthogonal group and the symplectic group explicitly. Schur-Horn's result can be stated in terms of a set of inequalities. The counterpart in the Lie-theoretic context is related to a partial ordering, introduced by Atiyah and Bott, defined on the closed fundamental Weyl chamber. Some results of Thompson on the diagonal elements of a matrix with prescribed singular values are recovered. Thompson-Poon's theorem on the convex hull of Hermitian matrices with prescribed eigenvalues is also generalized. Then a result of Atiyah-Bott is recovered. 相似文献
18.
Yoshihiro Maruyama 《Annals of Pure and Applied Logic》2010,161(12):1486-1501
Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: (1) the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well as a dual adjunction between the category of convexity algebras and the category of convexity spaces; (2) the latter notion of point induces a dual equivalence between the category of “m-spatial” convexity algebras and the category of “m-sober” convexity spaces. We finally argue that the former notion of a point is more useful than the latter one from a category theoretic point of view and that the former notion of a point actually represents a polytope (or generic point) and the latter notion of a point properly represents a point. We also remark on the close relationships between pointfree convex geometry and domain theory. 相似文献
19.
给出赋Luxemburg范数的Orlicz函数空间的紧一致凸、弱紧一致凸、紧局部一致凸、弱紧局部一致凸和k-drop凸的判据,并且据此得到在Orlicz函数空间中这些凸性的等价关系. 相似文献