The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization

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...

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Bibliographic Details
Published in:PloS one 2023-07, Vol.18 (7), p.e0274497-e0274497
Main Authors: Su, Ke, Liu, Shaohua, Lu, Wei
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Computer and Information Sciences
Convergence
Health aspects
Iterative methods
Lagrange multiplier
Linear systems
Mathematical optimization
Methods
Minimax technique
Optimization
Penalty function
Physical Sciences
Quadratic programming
Research and Analysis Methods
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0274497