On an algorithm in nondifferential convex optimization

• Main Authors: Đuranović-Miličić Nada I., Gardašević-Filipović Milanka
• Format: Article
• Language: English
• Published: University of Belgrade 2013-01-01
• Series: Yugoslav Journal of Operations Research
• Subjects: Moreau-Yosida regularization; non-smooth convex optimization; directional derivative; second order Dini upper directional derivative; uniformly convex functions
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-0243/2013/0354-02431200024D.pdf

In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.