In this paper, we mainly study the Abadie constraint qualification (ACQ) and the strong ACQ of a convex multifunction. To characterize the general difference between strong ACQ and ACQ, we prove that the strong ACQ is essentially equivalent to the ACQ plus the finite distance of two image sets of the tangent derivative multifunction on the sphere and the origin, respectively. This characterization for the strong ACQ is used to provide the exact calmness modulus of a convex multifunction. Finally, we apply these results to local and global error bounds for a convex inequality defined by a proper convex function. The characterization of the strong ACQ enables us to give primal equivalent criteria for local and global error bounds in terms of contingent cones and directional derivatives.

在本文中，我们主要研究Abadie约束条件（ACQ）和凸多功能的强ACQ。为了表征强ACQ和ACQ之间的一般差异，我们证明了强ACQ实质上等于ACQ加上球面和原点上切线导数多功能的两个图像集的有限距离。强ACQ的这种特征可用于提供凸多功能的精确的平静模量。最后，我们将这些结果应用于由适当凸函数定义的凸不等式的局部和全局误差范围。强大的ACQ的特征使我们能够根据或然锥和方向导数给出局部和全局误差范围的原始等效标准。