On the isolated calmness property of implicitly defined multifunctions

From calmness to Hoffman constants for linear semi-infinite inequality systems

In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand side. The Hoffman modulus is shown to coincide with the supremum of Lipschitz upper semicontinuity and calmness moduli when confined to multifunctions with a c…

On Lipschitzian properties of implicit multifunctions

The paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool one employs the directional limiting coderivative which, together with the graphical derivative, enable us a fine analysis of the local behavior of the investigated multifunction along relevant directions. For verification of the calmness property, in addition, a new condition has been discovered which parallels the missing implicit function paradigm and permits us to replace the original multifunction by a substantially simpler one. Moreove…

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On Lipschitzian properties of multifunctions defined implicitly by "split" feasibility problems

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An implicit multifunction theorem for the hemiregularity of mappings with application to constrained optimization

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative stability property for set-valued mappings is motivated by applications to the penalization of constrained optimization problems, through the notion of problem calmness. As a main result, an implicit multifunction theorem for parameterized inclusion problems is established, which measures the uniform hemiregularity of the related solution mapping in terms of probl…

由“分裂”可行性问题隐式定义的多值函数的一阶近似及其在优化中的应用

First-order approximations of multifunctions defined implicitly by "split" feasibility problems with applications to optimization

本文研究参数化“分裂”可行性问题的解映射（多值函数）的一阶微分性质，给出其图形导数的内外近似，并探讨其在带“分裂”可行性约束的数学规划最优性条件构建中的应用。

On Differential Properties of Multifunctions Defined Implicitly by Set-Valued Inclusions

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…