A smoothing approach forsemi-infinite programming with projected Newton-type algorithm

Zhi Guo Feng; Kok Lay Teo; Volker Rehbock

doi:10.3934/jimo.2009.5.141

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2009, Volume 5, Issue 1: 141-151. Doi: 10.3934/jimo.2009.5.141

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

1.
College of Mathematics and Computer Science, Chongqing Normal University, Chongqing
2.
Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845
3.
Curtin University of Technology, Bentley WA

Received: December 31, 2007

Revised: June 30, 2008

Published: December 2008

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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.

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Mathematics Subject Classification: Primary: 90C34; Secondary: 90C5.

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