The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax
Ke Su1, Shaohua Liu1, Wei Lu1
1Key Laboratory of Machine Learning and Computational Intelligence Baoding, College of Mathematics and Information Science, Hebei University, Baoding, China.
Abstract:
In this paper, we proposed an adaptive QP-free method without a penalty function or a filter for minimax optimization. In each iteration, solved two linear systems of equations constructed from Lagrange multipliers and KKT-conditioned NCP functions. Based on the work set, the computational scale is further reduced. Instead of the filter structure, we adopt a nonmonotonic equilibrium mechanism with an adaptive parameter adjusted according to the result of each iteration. Feasibility of the algorithm are given, and the convergence under some assumptions is demonstrated. Numerical results and practical application are reported at the end.
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