TY - JOUR
T1 - Stability for Constrained Minimax Optimization
AU - Dai , Yu-Hong
AU - Zhang , Liwei
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 542
EP - 565
PY - 2023
DA - 2023/04
SN - 4
DO - http://doi.org/10.4208/csiam-am.SO-2021-0040
UR - https://global-sci.org/intro/article_detail/csiam-am/21641.html
KW - Constrained minimax optimization, Jacobian uniqueness conditions, strong regularity, strong sufficient optimality condition, Kojima mapping, local Lipschitzian homeomorphism.
AB - <p style="text-align: justify;">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 $\mathcal{C}^2$ 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.</p>