论文标题
关于由设定值夹层隐式定义的多种函数的差异特性
On Differential Properties of Multifunctions Defined Implicitly by Set-Valued Inclusions
论文作者
论文摘要
在本文中，通过各种分析技术研究了由集合价值夹层隐式定义的多个多功能衍生物的几种属性。设定值的包含物是正式化锥体约束系统实现的问题，该系统的数据受到不确定元素的“粗略知识”的影响，因此无法将其施放在传统的通用方程式中。 这项研究的重点是与Lipschitzian特性开始的参数化设置值包含相关的解决方案映射的一阶行为，然后考虑其图形衍生物。特别是，解决方案映射的Aubin连续性的条件是根据定义包含的集合值映射的外部预先细分的。一类参数化的集合值振动被选出，其解决方案映射原来是凸。探索了图形衍生物的一些相关后果。在不存在的情况下，通过问题数据的预肽提供了图形衍生物的内部和外部近似的公式。还可以通过绩效函数的亚差异获得来计算解决方案映射的代码绘制的表示形式。
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the robust fulfilment of cone constraint systems, whose data are affected by a "crude knowledge" of uncertain elements, so they can not be casted in traditional generalized equations. The focus of this study in on the first-order behaviour of the solution mapping associated with a parameterized set-valued inclusion, starting with Lipschitzian properties and then considering its graphical derivative. In particular, a condition for the Aubin continuity of the solution mapping is established in terms of outer prederivative of the set-valued mapping defining the inclusion. A large class of parameterized set-valued inculsions is singled out, whose solution mapping turns out to be convex. Some relevant consequences on the graphical derivative are explored. In the absence of that, formulae for the inner and outer approximation of the graphical derivative are provided by means of prederivatives of the problem data. A representation useful to calculate the coderivative of the solution mapping is also obtained via the subdifferential of a merit function.
