论文标题
相对于一套和广义的mordukhovich标准，类似Lipschitz的特性
Lipschitz-like property relative to a set and the generalized Mordukhovich criterion
论文作者
论文摘要
在本文中，我们将分别为设定值映射建立一些必要的条件和足够的条件，以使类似Lipschitz的属性相对于封闭设置，并通过使用常规正常锥和限制了设置值映射的限制图的正常锥体。我们将获得一个设定值映射的完整表征，以使Lipschitz-property相对于封闭式和凸的封闭式构图，该代码层的投影在切线锥上的投影。此外，通过引入设定值映射的投影代码，我们建立了相对于封闭和凸集的Lipschitz样属性的可验证的通用Mordukhovich标准。我们将使用相应的投影代码鉴定值的外部规范来研究集合值映射的图形模量的表示。对于扩展的实价函数，我们将应用所获得的结果来研究其LIPSCHITZ的连续性相对于封闭式和凸集，以及相对于半线的级别映射的Lipschitz样性质。
In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone. Furthermore, by introducing a projectional coderivative of set-valued mappings, we establish a verifiable generalized Mordukhovich criterion for the Lipschitz-like property relative to a closed and convex set. We will study the representation of the graphical modulus of a set-valued mapping relative to a closed and convex set by using the outer norm of the corresponding projectional coderivative value. For an extended real-valued function, we will apply the obtained results to investigate its Lipschitz continuity relative to a closed and convex set and the Lipschitz-like property of a level-set mapping relative to a half line.
