ACCPM - A Library for Convex Optimization Based on an Analytic Center Cutting Plane Method

Introduction We are concerned in this note with the Goffin Haurie and Vial's [7] Analytic Center Cutting Plane Method (ACCPM for short) for large-scale convex optimization. Its state-of-the-art implementation [10] is now available upon request for academic research use. Cutting plane methods for convex optimization have a long history that goes back at least to a fundamental paper of Kelley [14]. There exist numerous strategies that can be applied to "solve" subsequent relaxed master problems in the cutting planes optimization scheme. In the Analytic Center Cutting Plane Method, subsequent relaxed master problems are not solved to optimality. Instead of it, an approximate analytic center of the current localization set is looked for. The theoretical development of ACCPM started from Goffin and Vial [9]. It was later continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several non