Minimizing the difference of convex and weakly convex functions via bundle method

We consider optimization problems with objective and constraint being the difference of convex and weakly convex functions. This framework covers a vast family of nonsmooth and nonconvex optimization problems, particularly those involving certain classes of composite and nonconvex value functions. We investigate several stationary conditions and extend the proximal bundle algorithm of [van Ackooij et … Read more

A unified analysis of descent sequences in weakly convex optimization, including convergence rates for bundle methods

We present a framework for analyzing convergence and local rates of convergence of a class of descent algorithms, assuming the objective function is weakly convex. The framework is general, in the sense that it combines the possibility of explicit iterations (based on the gradient or a subgradient at the current iterate), implicit iterations (using a … Read more