Empirical and Theoretical Comparisons of Several Nonsmooth Minimization Methods and Software

The most of nonsmooth optimization methods may be divided in two main groups: subgradient methods and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. In this report we test and compare both different bundle methods and different subgradient methods as well as some methods which may be considered as hybrids of these two and/or some others. All the solvers tested are so-called general black box methods which, at least in theory, can be used to solve almost all kinds of problems. The test set included large amount of different unconstrained nonsmooth minimization problems. That is, for instance, convex and nonconvex problems, piecewise linear and quadratic problems and problems with different sizes. The aim of this work is not to foreground some method over the others but to get some kind of insight which kind of method to select for certain types of problems.