New limited memory bundle method for large-scale nonsmooth optimization

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables. In such problems, the direct application of smooth gradient-based methods may lead to a failure due to the nonsmooth nature of the problem. On the other hand, none of the current general nonsmooth optimization methods is efficient in large-scale settings. In this article, we describe a new limited memory variable metric based bundle method for nonsmooth large-scale optimization. In addition, we introduce a new set of academic test problems for large-scale nonsmooth minimization. Finally, we give some encouraging results from numerical experiments using both academic and practical test problems.