Subgradient and Bundle Methods for Nonsmooth Optimization
The nonsmooth optimization methods can mainly be divided into two groups: subgradient and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. The goal of this work is to test and compare different bundle and subgradient methods as well as some hybrids of these two and/or some others. The test set included a large amount of different unconstrained nonsmooth minimization problems, e.g., convex and nonconvex problems, piecewise linear and quadratic problems, and problems with different sizes. Rather than foreground some method over the others, our aim is to get some insight on which method is suitable for certain types of problems.
KeywordsDescent Direction Quadratic Problem Bundle Method Subgradient Method Nonconvex Problem
We would like to acknowledge professors A. Kuntsevich and F. Kappel for providing Shor’s r-algorithm in their web-page as well as professors L. Lukšan and J. Vlček for providing the bundle-Newton algorithm. The work was financially supported by the University of Turku (Finland) and the University of Ballarat (Australia) and the Australian Research Council.
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