Abstract: An implementable bundle method for unconstrained nonsmooth convex optimization problem is provided in this paper. At first, a general bundle method is given. Next, a new update strategy for the proximal parameter is proposed. At the $k$th iteration, if the actual descent is close to the predicted one, the proximal parameter is enlarged; otherwise, it is decreased. Then, an implementable bundle method is proposed, which combines the subgradient aggregation strategy with the proximal parameter update strategy. At the same time, its convergence analysis is given as well. Finally, two numerical examples are presented to show the validity of the algorithm  proposed in this paper.

Key words: nonsmooth optimization, convex programming, bundle method