Year: 2023
Author: Yu-Hong Dai, Liwei Zhang
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 3 : pp. 542–565
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0040
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 3 : pp. 542–565
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Constrained minimax optimization Jacobian uniqueness conditions strong regularity strong sufficient optimality condition Kojima mapping local Lipschitzian homeomorphism.