In this paper, the notion of graphical derivatives is applied to define a new class of several well-known constraint qualifications for a nonconvex multifunction M at a point of its graph. This class is called as “scaled constraint qualifications”. The reason of this terminology is that these conditions ensure the existence of bounded KKT multiplier vectors with a proper upper bound. The relations between these constraint qualifications and stability properties of M are also investigated. New sharp necessary optimality conditions with bounded multiplier vectors are derived for an optimization problem with a generalized equation constraint. The results are adapted to nonsmooth general constrained problems and nonsmooth mathematical programs with equilibrium constraints.

中文翻译：

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广义方程约束问题的比例约束条件及其在具有平衡约束的非光滑数学程序中的应用

在本文中，使用图形导数的概念为非凸多功能M的一个点定义了几类新的约束条件。此类称为“缩放约束条件”。该术语的原因是，这些条件确保了具有合适上限的有界KKT乘数向量的存在。还研究了这些约束条件与M的稳定性之间的关系。针对具有广义方程约束的优化问题，推导了具有有界乘法器矢量的新的尖锐必要最优性条件。结果适用于具有约束约束的非光滑一般约束问题和非光滑数学程序。