集值包含隐含定义的集值函数的微分性质
On Differential Properties of Multifunctions Defined Implicitly by Set-Valued Inclusions
摘要：
本文利用变分分析方法研究了由集值包含隐式定义的集值函数的广义导数的若干性质。集值包含是锥约束系统鲁棒实现的形式化问题，其数据受不确定元素的“粗糙知识”影响，不能用传统的广义方程表示。本研究的重点是在一阶行为的解决方案映射与参数化集值包含，从Lipschitzian属性，然后考虑其图形的衍生物。特别地，一个条件的Aubin连续的解决方案映射建立在定义的包含集值映射的外预导数。本文提出了一大类参数集值灌输，证明了其解映射是凸的。一些相关的后果的图形衍生物进行了探讨。在没有的情况下，公式的内部和外部近似的图形衍生物提供了通过预衍生的问题数据。一个表示有用的计算的解映射的协导数也得到了通过次微分的价值函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
