An Active Set Smoothing Method for Solving Unconstrained Minimax Problems
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-06-24
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
In this paper, an active set smoothing function based on the plus function is constructed for the maximum function.
The active set strategy used in the smoothing function reduces the number of gradients and Hessians evaluations of the component functions in the optimization.
Combing the active set smoothing function, a simple adjustment rule for the smoothing parameters, and an unconstrained minimization method, an active set smoothing method is proposed for solving unconstrained minimax problems.
The active set smoothing function is continuously differentiable, and its gradient is locally Lipschitz continuous and strongly semismooth.
Under the boundedness assumption on the level set of the objective function, the convergence of the proposed method is established.
Numerical experiments show that the proposed method is feasible and efficient, particularly for the minimax problems with very many component functions.
American Psychological Association (APA)
Zhou, Zhengyong& Yang, Qi. 2020. An Active Set Smoothing Method for Solving Unconstrained Minimax Problems. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1202004
Modern Language Association (MLA)
Zhou, Zhengyong& Yang, Qi. An Active Set Smoothing Method for Solving Unconstrained Minimax Problems. Mathematical Problems in Engineering No. 2020 (2020), pp.1-25.
https://search.emarefa.net/detail/BIM-1202004
American Medical Association (AMA)
Zhou, Zhengyong& Yang, Qi. An Active Set Smoothing Method for Solving Unconstrained Minimax Problems. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1202004
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1202004