Using Analytic Center and Cutting Planes Methods for Nonsmooth Convex Programming

We propose a method for unconstrained minimization of nondifferentiable convex functions. At each iteration, the algorithm includes a reinitialization procedure, due to a knew cut, and some iterations of the analytic center method, those necessary to lower the upper bound of the best iterate function value. The convergence and the polynomial complexity by iteration are established, and numerical tests with typical problems from the literature are presented. The results are similar to those obtained by bundle methods and the algorithms that use analytic center.