A proximal bundle method based on approximate subgradients. (English) Zbl 1054.90053

Hintermüller, Michael

Comput. Optim. Appl. 20, No. 3, 245-266 (2001).

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.

MSC:

90C25	Convex programming
49J52	Nonsmooth analysis

Keywords:

approximate subgradient; convex programming; nonsmooth optimization; proximal bundle method