A proximal bundle method based on approximate subgradients

In this paper a proximal bundle method is introduced that is capable to dea l with approximate subgradients. No further knowledge of the approximation quality (like explicit knowledge or controllability of error bounds) is req uired for proving convergence. It is shown that every accumulation point of the sequence of iterates generated by the proposed algorithm is a well-def ined approximate solution of the exact minimization problem. In the case of exact subgradients the algorithm behaves like well-established proximal bu ndle methods. Numerical tests emphasize the theoretical findings.