  This paper establishes the iteration-complexity of proximal bundle methods
for solving hybrid (i.e., a blend of smooth and nonsmooth) weakly convex
composite optimization (HWC-CO) problems. This is done in a unified manner by
considering a proximal bundle framework (PBF) based on a generic bundle update
scheme which includes various well-known bundle update schemes. In contrast to
other wellknown stationary conditions in the context of HWC-CO, PBF uses a new
stationarity measure which is easily verifiable and, at the same time, implies
any of the former ones.
