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广义度量S-KKM映射的性质及其对鞍点问题的应用 总被引:3,自引:0,他引:3
引入了S为集盥映射情况下的广义度量S-KKM映射和超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射原理和广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的Ky Fan极大极小不等式和鞍点定理. 相似文献
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在半连续前提下,给出凸函数和严格凸函数的不等式刻划.指出非空凸集上的半连续函数满足中间点凸性时,成为凸函数,满足中间点严格凸性时,成为严格凸函数.最后定义F—G广义凸函数和条件p1,p2等概念,列举若干满足条件p1,p2的数量函数和向量函数,并指出,对于F—G广义凸函数,在条件p1,p2及一定连续性条件下,可以得到类似结果. 相似文献
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一类广义变换半群的格林关系 总被引:1,自引:0,他引:1
设X是一个全序集,E是X上的一个凸等价关系.令
OE(X)={f∈TE(X):Ax,y∈X,x≤y→f(x)≤f(y)),
其中TE(X)是E-保持变换半群.对于取定的θ∈OE(X),在OE(X)上定义运算fog=fθg,使OE(X)成为广义半群OE(X;θ).对于有限全序集X上的凸等价关系E,本文刻画了广义半群OE(X;θ)的正则元,描述了这个半群的格林关系. 相似文献
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Ky Fan点集的本质连通区 总被引:8,自引:1,他引:7
本文首先引入了Ky Fan点集本质连能区的概念,证明了对任一满足一定凸性和连续性条件的函数,其Ky Fan点集至少存在一个本质连能区.作为应用,我们推出地任何一般n人非合伯对策(其支付函数满足一些凸性和连续性条件),其Nash平衡点集至少存在一个本质连通区. 相似文献
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广义度量S-KKM映射的性质及其对变分不等式的应用 总被引:3,自引:0,他引:3
文开庭 《纯粹数学与应用数学》2009,25(1):152-156
引入了超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的KyFan极大极小不等式和鞍点定理. 相似文献
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在实赋范空间上通过范数导数(左、右两个)引进一种广义内积(上、下两个),并用它们对实赋范空间上的线性连续泛函给出上、下估计式。本文主要结果揭示了实赋范空间上的如下三类连续线性泛函的统一性。第一类连续线性泛函是指其中每一个f都在闭单位球上取到其范数值f。第二类连续线性泛函是指其中第一个f的核Ker(f)与另一空间元素之间的最佳逼近元存在。第三类连续性泛函是指其中每一个f的上限和下限分别可用上、下两种 相似文献
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Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized through the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions. 相似文献
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Mirosaw Adamek Attila Gilnyi Kazimierz Nikodem Zsolt Ples 《Journal of Mathematical Analysis and Applications》2007,330(2):829-835
The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363–371] is extended to the two-dimensional case. Using three-parameter families, we define generalized convex (midconvex, M-convex) functions and show some continuity properties of them. 相似文献
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提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性. 相似文献
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Jean-Paul Penot 《Journal of Global Optimization》2008,40(1-3):319-338
We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter
sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special
structure. We examine several examples. In particular, we consider some special classes of generalized convex functions. 相似文献
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1.IntroductionConsidersmoothcompositionsofmax-typefunctionsoftheform:f(x)=g(x,aestfij(x),'',,T?:fmj(x)),(1.1)wherexER",Ji,i~1,'',marefiniteindexsets,gandfij,jEJi,i=1,'',marecontinuouslydifferentiableonRill 71andR;'respectively.Thisclassofnonsmoothfunct… 相似文献
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《Optimization》2012,61(7):943-959
We study some classes of generalized convex functions, using a generalized differential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdifferential or a pseudo-differential in the sense of Jeyakumar and Luc. Such a general framework allows us to avoid technical assumptions related to specific constructions. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced. We devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange–Kuhn–Tucker multipliers for mathematical programming problems. 相似文献
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《Optimization》2012,61(2):305-319
The scalarization functions were used in vector optimization for a long period. Similar functions were introduced and used in economics under the name of shortage function or in mathematical finance under the name of (convex or coherent) measures of risk. The main aim of this article is to study Lipschitz continuity properties of such functions and to give some applications for deriving necessary optimality conditions for vector optimization problems using the Mordukhovich subdifferential. 相似文献