共查询到20条相似文献,搜索用时 46 毫秒
1.
Tudor Zamfirescu 《Set-Valued Analysis》2000,8(3):295-297
We introduce the notion of a starshaped set-valued function, and relate it to convex set-valued functions. We prove a theorem which, in the convex case, implies that single-valuedness is exceptional if the function is not everywhere single-valued. A second result shows a remarkable costantness of images for starshaped set-valued functions. Both theorems were inspired from a result of Deutsch and Singer, which they strengthen. 相似文献
2.
Andreas H. Hamel 《Set-Valued and Variational Analysis》2009,17(2):153-182
It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space
is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre–Fenchel conjugates for set-valued
functions is introduced and a Moreau–Fenchel theorem is proven. Examples and applications are given, among them a dual representation
theorem for set-valued convex risk measures.
相似文献
3.
Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities 总被引:3,自引:0,他引:3
The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem. 相似文献
4.
Nicolae Popovici 《Journal of Global Optimization》2007,38(1):103-118
The principal aim of this paper is to extend some recent results concerning the contractibility of efficient sets and the
Pareto reducibility in multicriteria explicitly quasiconvex optimization problems to similar vector optimization problems
involving set-valued objective maps. To this end, an appropriate notion of generalized convexity is introduced for set-valued
maps taking values in a partially ordered real linear space, which naturally extends the classical concept of explicit quasiconvexity
of real-valued functions. Actually, the class of so-called explicitly cone-quasiconvex set-valued maps in particular contains
the cone-convex set-valued maps, and it is contained in the class of cone-quasiconvex set-valued maps.
相似文献
5.
L. Kuntz 《Journal of Optimization Theory and Applications》1995,86(1):263-270
A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1). 相似文献
6.
Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems 总被引:20,自引:6,他引:14
This paper gives several characterizations of nearly subconvexlike set-valued maps (see Ref. 1) and shows that a weakly efficient solution and a Benson properly efficient solution of a vector optimization problem with nearly-subconvexlike objectives and constraints can be expressed in terms of saddle points defined in a suitable sense. 相似文献
7.
We give a new existence theorem for loose saddle point of set-valued map having values in a partially ordered topological vector space which is based on continuity and quasiconvexity- quasiconcavity of its scalarized maps. Moreover, we prove a new saddle point theorem for vector-valued functions in locally convex topological vector spaces under weak condition that is the semicontinuity of two function scalarization. 相似文献
8.
S. K. Mishra S. Y. Wang K. K. Lai 《Journal of Optimization Theory and Applications》2008,138(1):77-84
Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In
this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities
(VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence
of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by
exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem.
The research of first author was partially supported by the Council of Scientific and Industrial Research, New Delhi, Ministry
of Human Resources Development, Government of India Grant 25(0132)/ER-II/2004. 相似文献
9.
In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings. 相似文献
10.
11.
T. H. Sweetser III 《Journal of Optimization Theory and Applications》1977,23(4):549-562
A set-valued derivative for a function at a point is a set of linear transformations whichapproximates the function near the point. This is stated precisely, and it is shown that, in general, there is not a unique minimal set-valued derivative for functions in the family of closed convex sets of linear transformations. For Lipschitz functions, a construction is given for a specific set-valued derivative, which reduces to the usual derivative when the function is strongly differentiable, and which is shown to be the unique minimal set-valued derivative within a certain subfamily of the family of closed convex sets of linear transformations. It is shown that this constructed set may be larger than Clarke's and Pourciau's set-valued derivatives, but that no irregularity is introduced.The author would like to thank Professor H. Halkin for numerous discussions of the material contained here. 相似文献
12.
The purpose of this paper is to introduce and study a class of set-valued variational inclusions in Banach spaces. By using Michael's selection theorem and Nadler's theorem, some existence theorems and iterative algorithms for solving this kind of set-valued variational inclusion in Banach spaces are established and suggested. 相似文献
13.
In this paper, we establish a decomposition theorem for polyharmonic functions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichlet problem for polyharmonic functions (PHD problem) and give a unified expression for a class of kernel functions associated with the solution in the case of the unit disc introduced by Begehr, Du and Wang. In addition, we also discuss some quasi-Dirichlet problems for homogeneous mixed-partial differential equations of higher order. It is worthy to note that the decomposition theorem in the present paper is a natural extension of the Goursat decomposition theorem for biharmonic functions. 相似文献
14.
F. Ventriglia 《Journal of Mathematical Analysis and Applications》2010,367(1):296-303
A Cafiero type criterion and an extension of the classical Dieudonné's theorem for a class of non-additive set functions valued into a complete Hausdorff uniform space are established. 相似文献
15.
《Optimization》2012,61(2):197-223
We consider functions with values in the power set of a pre-ordered, separated locally convex space with closed convex images. To each such function, a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre–Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. To the set-valued conjugate, a full calculus is provided, including a biconjugation theorem, a chain rule and weak and strong duality results of the Fenchel–Rockafellar type. 相似文献
16.
A new class of set-valued maps that includes all upper and lower semicontinuous set-valued maps is introduced. For this class,
a selection theorem having applications in the theory of differential inclusions is presented.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 503–507, October, 1999. 相似文献
17.
在赋范线性空间中借助切导数研究集值优化问题的严有效性.当目标函数和约束函数相对于同一向量函数为拟不变凸时,利用凸集分离定理给出了集值优化问题取得严有效元的Kuhn—Xhcker型最优陛必要条件.利用切导数的性质,用构造性方法得到了拟不变凸集值优化问题取得严有效元的充分条件. 相似文献
18.
集值变分不等式问题的例外簇 总被引:3,自引:0,他引:3
本文首先在Banach空间中证明了零调集值映射的一个Leray-Schauder型不动点定理,然后在Hilbert空间中定义了零调集值映射的变分不等式的例外簇,利用本文给出的不动点定理给出了无界集上的变分不等式问题存在解的一个充分条件.此条件弱于许多已知的关于变分不等式问题的解的存在性条件,并由此得到Hilbert空间中几个变分不等式约解的存在性定理. 相似文献
19.
In real ordered linear spaces, an equivalent characterization of generalized cone subconvexlikeness of set-valued maps is firstly established. Secondly, under the assumption of generalized cone subconvexlikeness of set-valued maps, a scalarization theorem of set-valued optimization problems in the sense of ?-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem of ?-global properly efficient element of set-valued optimization problems is obtained. The results in this paper generalize and improve some known results in the literature. 相似文献
20.
G -凸空间中的广义对策和广义矢量拟平衡问题组 总被引:2,自引:0,他引:2
丁协平 《数学物理学报(A辑)》2006,26(4):506-515
该文在广义G -凸空间中引入并研究了一类新的广义矢量拟平衡问题组(SGVQEP).利用作者的一族集值映象的极大元存在定理,证明了广义对策的一个新的平衡存在定理.作为应用,在非紧乘积G -凸空间中证明了SGVQEP解的一些新的存在定理. 相似文献