On Lipschitzian Properties of Implicit Multifunctions
本文为隐式多值函数的平静性和Aubin性质开发了新的充分条件，利用方向极限余导数进行精细分析，并发现了一个平行于缺失隐函数范式的新条件，可用于简化原多值函数。
This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivative which, together with the graphical derivative, enables 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. Moreover, as an auxiliary tool, a handy formula for the computation of the directional limiting coderivative of the normal-cone map with a polyhedral set has been derived which perfectly matches the framework of [A. L. Dontchev and R. T. Rockafellar, SIAM J. Optim., 6 (1996), pp. 1087--1105]. All important statements are illustrated by examples.