Nonsmooth optimization is traditionally based on convex analysis and most solution
methods rely strongly on the convexity of the problem. In this paper, we propose an
efficient diagonal bundle method for nonconvex large-scale nonsmooth optimization.
The novelty of the new method is in different usage of metrics depending on the convex
or concave behaviour of the objective at the current iteration point. The usage
of different metrics gives us a possibility to better deal with the nonconvexity of the
problem than the sole — the most commonly used and quite arbitrary — downward
shifting of the piecewise linear model does. The convergence of the proposed method
is proved for semismooth functions that are not necessary differentiable nor convex.
The numerical experiments have been made using problems with up to million variables.
The results to be presented confirm the usability of the new method.