Codifferential method for minimizing nonsmooth DC functions

Authors:
A. M. Bagirov;J. Ugon
Affiliations:
Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia 3353;Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia 3353
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

In this paper, a new algorithm to locally minimize nonsmooth functions represented as a difference of two convex functions (DC functions) is proposed. The algorithm is based on the concept of codifferential. It is assumed that DC decomposition of the objective function is known a priori. We develop an algorithm to compute descent directions using a few elements from codifferential. The convergence of the minimization algorithm is studied and its comparison with different versions of the bundle methods using results of numerical experiments is given.