A nonsmooth Levenberg-Marquardt method for solving semi-infinite programming problems

Autores: Cheng Ma, Changyu Wang
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 2, 2009, págs. 633-642
Idioma: inglés
DOI: 10.1016/j.cam.2009.01.004
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Resumen
- In this paper, we first transform the semi-infinite programming problem into the KKT system by the techniques in [D.H. Li, L. Qi, J. Tam, S.Y. Wu, A smoothing Newton method for semi-infinite programming, J. Global. Optim. 30 (2004) 169�194; L. Qi, S.Y. Wu, G.L. Zhou, Semismooth Newton methods for solving semi-infinite programming problems, J. Global. Optim. 27 (2003) 215�232]. Then a nonsmooth and inexact Levenberg�Marquardt method is proposed for solving this KKT system based on [H. Dan, N. Yamashita, M. Fukushima, Convergence properties of the inexact Levenberg�Marquardt method under local error bound conditions, Optimim. Methods Softw., 11 (2002) 605�626]. This method is globally and superlinearly (even quadratically) convergent. Finally, some numerical results are given.