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Journal of Applied Mathematics
Volume 2014, Article ID 852074, 7 pages
Research Article

A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems

Li Dong,1 Bo Yu,2,3 and Yu Xiao4

1College of Science, Dalian Nationalities University, Dalian 116600, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
3School of Sciences, Dalian University of Technology, Dalian at Panjin 124221, China
4School of Basic Science, East China Jiaotong University, Nanchang 330013, China

Received 20 May 2014; Accepted 30 June 2014; Published 17 July 2014

Academic Editor: Mariano Torrisi

Copyright © 2014 Li Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on discretization methods for solving semi-infinite programming problems, this paper presents a spline smoothing Newton method for semi-infinite minimax problems. The spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; that is, it introduces an active set technique, so it is more efficient for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. Numerical tests show that the new method is very efficient.