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

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.