@article{1054.90053,
author="Hinterm\"uller, Michael",
title="{A proximal bundle method based on approximate subgradients.}",
language="English",
journal="Comput. Optim. Appl. ",
volume="20",
number="3",
pages="245-266",
year="2001",
doi={10.1023/A:1011259017643},
abstract="{Summary: A proximal bundle method is introduced that is capable to
    deal with approximate subgradients. No further knowledge of the
    approximation quality (like explicit knowledge or controllability of error
    bounds) is required for proving convergence. It is shown that every
    accumulation point of the sequence of iterates generated by the proposed
    algorithm is a well-defined approximate solution of the exact minimization
    problem. In the case of exact subgradients the algorithm behaves like
    well-established proximal bundle methods. Numerical tests emphasize the
    theoretical findings.}",
keywords="{approximate subgradient; convex programming; nonsmooth optimization;
    proximal bundle method}",
classmath="{*90C25 (Convex programming)
49J52 (Nonsmooth analysis (other weak concepts of optimality))
}",
}