A Proximal Bundle Method for Nonconvex Functions with Inexact Oracles

For a class of nonconvex nonsmooth functions, we consider the problem of computing an approximate critical point, in the case of inexact oracles. The latter means that only an inexact function value and an inexact subgradient are available, at any given point. We assume that the errors in function and subgradient evaluations are merely bounded, and in principle need not vanish in the limit. We examine the redistributed proximal bundle approach in this setting, and show that reasonable convergence properties are obtained. We further consider a battery of difficult nonsmooth nonconvex problems, made even more difficult by introducing noise in the oracle output. We verify that very satisfactory outcomes are obtained in our computational implementation of the inexact algorithm.