Globally convergent limited memory bundle method for large-scale nonsmooth optimization

Authors:
Napsu Haarala;Kaisa Miettinen;Marko M. Mäkelä
Affiliations:
School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, 2050, Johannesburg, Wits, South Africa;Helsinki School of Economics, P.O. Box 1210, 00101, Helsinki, Wits, Finland;Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), 40014, Helsinki, Wits, Finland
Venue:
Mathematical Programming: Series A and B
Year:
2007

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Abstract

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of thousands of variables. In the paper [Haarala, Miettinen, Mäkelä, Optimization Methods and Software, 19, (2004), pp. 673–692] we have described an efficient method for large-scale nonsmooth optimization. In this paper, we introduce a new variant of this method and prove its global convergence for locally Lipschitz continuous objective functions, which are not necessarily differentiable or convex. In addition, we give some encouraging results from numerical experiments.