A VERSION OF THE BUNDLE IDEA FOR MINIMIZING A NONSMOOTH FUNCTION: CONCEPTUAL IDEA, CONVERGENCE ANALYSIS, NUMERICAL RESULTS

During recent years various proposals for the minimization of a nonsmooth functional have been made. Amongst these, the bundle concept turned out to be an especially fruitful idea. Based on this concept, a number of authors have developed codes that can successfully deal with nonsmooth problems. The aim of the paper is to show that, by adding some features of the trust region philosophy to the bundle concept, the end result is a distinguished member of the bundle family with a more stable behaviour than some other bundle versions. The reliability and efficiency of this code is demonstrated on the standard academic test examples and on some real-life problems.