Journal of Industrial and Management Optimization (JIMO)

A smoothing approach for semi-infinite programming with projected Newton-type algorithm

Pages: 141 - 151, Volume 5, Issue 1, February 2009      doi:10.3934/jimo.2009.5.141

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Zhi Guo Feng - College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China (email)
Kok Lay Teo - Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845, Australia (email)
Volker Rehbock - Curtin University of Technology, Bentley WA, Australia (email)

Abstract: In this paper we apply the projected Newton-type algorithm to solve semi-infinite programming problems. The infinite constraints are replaced by an equivalent nonsmooth function which is then approximated by a smoothing function. The KKT system is formulated as a nonsmooth equation. We then apply the projected Newton-type algorithm to solve this equation and show that the accumulation point satisfies the KKT system. Some numerical results are presented for illustration.

Keywords:  KKT system, Projected Newton-type algorithm, Smoothing function.
Mathematics Subject Classification:  Primary: 90C34; Secondary: 90C5.

Received: January 2008;      Revised: July 2008;      Available Online: December 2008.