Limited memory bundle algorithm for inequality constrained nondifferentiable optimization

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable metric bundle method and the smooth limited memory variable metric method, and the constraint handling is based on the primal-dual feasible direction interior point approach. The preliminary numerical experiments to be presented confirm the effectiveness of the method.