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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 145083, 11 pages
http://dx.doi.org/10.1155/2012/145083
Research Article

An Augmented Lagrangian Algorithm for Solving Semiinfinite Programming

1Department of Mathematics, Shandong Normal University, Jinan, China
2Institute for Operations Research, Qufu Normal University, Qufu, China

Received 16 July 2012; Accepted 12 September 2012

Academic Editor: Jian-Wen Peng

Copyright © 2012 Qian Liu and Changyu Wang. 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.

Abstract

We present a smooth augmented Lagrangian algorithm for semiinfinite programming (SIP). For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence generated by the algorithm is the solution of SIP. We get this global convergence result without any boundedness condition or coercive condition. Another corollary of the perturbation theorem shows that the perturbation function at zero point is lower semi-continuous if and only if the algorithm forces the sequence of objective function convergence to the optimal value of SIP. Finally, numerical results are given.