共查询到18条相似文献,搜索用时 125 毫秒
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引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分. 相似文献
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主要研究了两类近似凸集的关系和性质.首先,举例说明两类近似凸集没有相互包含关系.其次,在近似凸集(nearly convex)条件下,证明了在一定条件下函数上图是近似凸集与凸集的等价关系.同时,考虑了近似凸函数与函数上图是近似凸集的等价刻画、近似凸函数与函数水平集是近似凸集的必要性,并用例子说明近似凸函数与函数水平集是近似凸集的充分性不成立.最后,基于近似凸函数和拟凸函数的概念,给出了近似拟凸函数的概念并研究了近似拟凸函数与水平集是近似凸集的等价刻画. 相似文献
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用算子刻划的亚纯单叶函数类 总被引:6,自引:0,他引:6
本文用算子刻划了亚纯星象函数、亚纯凸象函数、亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质。 相似文献
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本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 . 相似文献
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研究了k-Hessian算子对应的多极点k-格林函数,得到了在k-超凸域上的连续性与边界行为,并通过Lelong-Jensen公式展示了k-Hessian边界测度与k-凸函数在极点处函数值之间的关系. 相似文献
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算子D~α及其刻划的亚纯p叶函数类 总被引:1,自引:0,他引:1
用算子Dα刻划了亚纯星象函数,亚纯凸象函数,亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质. 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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《Applied Mathematics Letters》2002,15(1):89-94
The polygonal containment problem is to position two structures of convex forms under rigid motion mechanics such that the forms of one structure are completely contained within the elements of the associated structure. In this note, the polygonal containment problem is formalized in terms of a generalized containment model and solved as a constrained nonlinear program. 相似文献
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引入了一个广义凸函数一高阶强Pre-invex函数,它是Guneer-Bhatia介绍的高阶强凸函数的一种推广.在此基础上,讨论并证明了高阶强Pre-invex函数的一些等价刻画,这些结论是Guneer-Bhatia给出结论的推广,扩大了凸函数的应用范围. 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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This paper addresses itself to the algorithm for minimizing the sum of a convex function and a product of two linear functions over a polytope. It is shown that this nonconvex minimization problem can be solved by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in higher dimension and apply a parametric programming (path following) approach. Also it is shown that the same idea can be applied to a generalized linear fractional programming problem whose objective function is the sum of a convex function and a linear fractional function. 相似文献
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H. Nakayama H. Sayama Y. Sawaragi 《Journal of Optimization Theory and Applications》1975,17(3-4):211-227
As is well known, a saddle point for the Lagrangian function, if it exists, provides a solution to a convex programming problem; then, the values of the optimal primal and dual objective functions are equal. However, these results are not valid for nonconvex problems.In this paper, several results are presented on the theory of the generalized Lagrangian function, extended from the classical Lagrangian and the generalized duality program. Theoretical results for convex problems also hold for nonconvex problems by extension of the Lagrangian function. The concept of supporting hypersurfaces is useful to add a geometric interpretation to computational algorithms. This provides a basis to develop a new algorithm. 相似文献