  Minimax optimization problems are an important class of optimization problems
arising from both modern machine learning and from traditional research areas.
We focus on the stability of constrained minimax optimization problems based on
the notion of local minimax point by Dai and Zhang (2020). Firstly, we extend
the classical Jacobian uniqueness conditions of nonlinear programming to the
constrained minimax problem and prove that this set of properties is stable
with respect to small $C^2$ perturbation. Secondly, we provide a set of
conditions, called Property A, which does not require the strict
complementarity condition for the upper level constraints. Finally, we prove
that Property A is a sufficient condition for the strong regularity of the
Kurash-Kuhn-Tucker (KKT) system at the KKT point, and it is also a sufficient
condition for the local Lipschitzian homeomorphism of the Kojima mapping near
the KKT point.
