共查询到20条相似文献,搜索用时 62 毫秒
1.
序扰动多目标规划的锥次微分稳定性 总被引:9,自引:1,他引:8
对于局部凸拓扑向量空间的多目标规划问题,本文研究并得到当确定空间序的控制锥受扰动,它们的锥有效点(解)集和锥弱有效点(解)集分别在锥次微分和锥弱次微分意义下的稳定性结果. 相似文献
2.
The theory of locally convex cones as a branch of functional analysis was presented by K. Keimel and W. Roth in [K. Keimel, W. Roth, Ordered Cones and Approximation, Lecture Notes in Math., vol. 1517, Springer-Verlag, Heidelberg, 1992]. We study some more results about dual cones and adjoint operators on locally convex cones. Moreover we introduce the concept of the uniformly precompact sets and discuss their relations with σ-bounded sets. Some results obtained about inductive limit, projective limit, metrizability and quotients of locally convex cones. 相似文献
3.
Vasile Postolica 《Journal of Global Optimization》1993,3(2):233-242
In this paper, the definition of supernormality for convex cones in locally convex spaces is discussed in detail on many interesting examples. Starting from the new direction for the study of the existence of efficient points (Pareto type optimums) in locally convex spaces offered by the concept of supernormal (nuclear) cone, we establish some existence results for the efficient points using boundedness and completeness of conical sections induced by non-empty subsets and we specify properties for the sets of efficient points beside important remarks 相似文献
4.
Zhou Feng 《数学年刊B辑(英文版)》1998,19(3):249-254
§1.IntroductionLetEbearealBanachspace,notnecesarilyreflexive.LetΦ,Ψ:E→]-∞,∞]betwolowersemicontinuousconvexfunctions.Wedenote... 相似文献
5.
We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling. 相似文献
6.
Dual characterizations of the set containments with strict cone-convex inequalities in Banach spaces
We give characterizations of the containment of a convex set either in an arbitrary convex set or in a set described by reverse
cone-convex inequalities in Banach spaces. The convex sets under consideration are the solution sets of an arbitrary number
of cone-convex inequalities, which can be either weak or strict inequalities. These characterizations provide ways of verifying
the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated
systems. 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 concept of evenly convex set is used to derive the dual conditions, characterizing the set containments.
相似文献
7.
近似锥-次类凸集值优化的严有效性 总被引:16,自引:0,他引:16
在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的严有效性.在近似锥-次类凸假设下,利用凸集分离定理,分别得到了Kuhn-Tucker型和Lagrange型最优性条件,建立了与(VP)等价的两种形式的无约束优化. 相似文献
8.
C. Zălinescu 《Mathematical Methods of Operations Research》1991,35(4):291-298
In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems. 相似文献
9.
1.IntroductionInthispaperwewillgivesomesuitablesufficientconditionswhichassuretheclosednesspropertyofthedifferenceoftwoclosedconvexsetsingeneralBanachspaces,notnecessarilyrenekive.Theclosednessproblemweareconcernedwithisfrequentlyencounteredindifferentbranchesofappliedmathematics;forexample,thesolvabilityoflinearsystemsoverconeandthedualitytheoryofabstractmathematicalprogramming.OurmotivationcomesfromaBaiocchi-Gastaldi-TomarelliIsresult13]concernedwiththecaseofHilbertspace.FurlhermorelK5th.… 相似文献
10.
关于多目标规划解的稳定性问题,一些学者在半连续意义下曾得到比较系统的结果.以后,在锥次微分意义下又获得了更深入的描述.近年,则进一步对目标和约束,以及确定目标空间序的控制锥均受扰动的多目标规划研究其解的稳定性问题,并在Banach空间和半连续的意义下,得到了很好的刻划.本文则对这类双扰动多目标规划问题,在局部凸拓扑向量空间和锥次微分的意义下,获得了相应的稳定性结论。 相似文献
11.
杨干山 《数学物理学报(A辑)》1997,(Z1)
该文首先给出了关于两个非紧凸集可被强分离的充分必要条件,它是[1,2]中一个定理的改进,然后利用它改进了[4-7]中一些定理和[8]中的一个结果. 相似文献
12.
Alessandro Savo 《Geometriae Dedicata》1998,73(2):181-214
We give a recursive algorithm for the computation of the complete asymptotic series, for small time, of the amount of heat inside a domain with smooth boundary in a Riemannian manifold; we consider arbitrary smooth initial data, and we impose Dirichlet condition on the boundary. When the Ricci curvature of the domain and the mean curvature of its boundary are both nonnegative, we also give sharp upper and lower bounds of the heat content which hold for all values of time. These estimates extend to convex sets of the Euclidean space having arbitrary boundary. 相似文献
13.
In a normed vector space, we study the minimal time function determined by a moving target set and a differential inclusion, where the set-valued mapping involved has constant values of a bounded closed convex set U. After establishing a characterization of ?-subdifferential of the minimal time function, we obtain that the limiting subdifferential of the minimal time function is representable by virtue of the corresponding normal cones of sublevel sets of the function and level or sublevel sets of the support function of U. The known results require the set U to have the origin as an interior point and the target set is a fixed set. 相似文献
14.
C. Zălinescu 《Optimization》2016,65(3):651-670
It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function. 相似文献
15.
16.
Antonio Leitão 《Numerical Functional Analysis & Optimization》2013,34(11):1153-1180
AbstractWe propose and analyze a family of successive projection methods whose step direction is the same as the Landweber method for solving nonlinear ill-posed problems that satisfy the Tangential Cone Condition (TCC). This family encompasses the Landweber method, the minimal error method, and the steepest descent method; thus, providing an unified framework for the analysis of these methods. Moreover, we define new methods in this family, which are convergent for the constant of the TCC in a range twice as large as the one required for the Landweber and other gradient type methods. The TCC is widely used in the analysis of iterative methods for solving nonlinear ill-posed problems. The key idea in this work is to use the TCC in order to construct special convex sets possessing a separation property, and to successively project onto these sets. Numerical experiments are presented for a nonlinear two-dimensional elliptic parameter identification problem, validating the efficiency of our method. 相似文献
17.
This paper deals with the problems of best approximation in β-normed spaces.With the tool of conjugate cone introduced in [1] and via the Hahn-Banach extension theorem of β-subseminorm in [2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of a β-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convex β-normed space must be Chebyshev is proved at last. 相似文献
18.
In this paper, we study properties of general closed convex sets that determine the closedness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones, strictly convex sets, and sets containing integer points in their interior. We then present a sufficient condition for the convex hull of integer points in general convex sets to be a polyhedron. This result generalizes the well-known result due to Meyer (Math Program 7:223–225, 1974). Under a simple technical assumption, we show that these sufficient conditions are also necessary for the convex hull of integer points contained in general convex sets to be a polyhedron. 相似文献
19.
In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex
cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational
inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems
is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones
depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of
vector complementarity problems, vector variational inequalities, and minimal element problems are also given.
While this paper was being revised in September 2006, Professor Alex Rubinov (the second author of the paper) left us due
to the illness. This is a very sad news to us. We dedicate this paper to the memory of Professor Rubinov as a mathematician
and truly friend. 相似文献
20.
In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to parameterized generalized equations governed by set-valued mappings with convex graphs. 相似文献