A new restricted memory level bundle method for constrained convex nonsmooth optimization

In this paper, a new restricted memory level bundle method for solving constrained convex nonsmooth optimization problems is proposed. To ensure convergence, the memory of our approach is restricted to at least two linearizations as well as a special linear function, while the traditional constrained bundle methods require at least four linearizations. Unusually, the new algorithm consists of outer loops and nested inner procedures, which can greatly facilitate the convergence analysis. In addition, a relaxed feasibility detection criterion is proposed, which may decrease the number of subproblems to be solved. Global convergence of the algorithm is established and an iteration complexity bound is derived. Finally, some preliminary numerical results show that the proposed method is efficient.