Oracle Based Optimization (OBO) conveniently designates an approach to handle a class of convex optimization problems in which the information pertaining to the function to be minimized and/or to the feasible set takes the form of a linear outer approximation revealed by an oracle. We show, through three representative examples, how difficult problems can be cast in this format, and solved. We present an efficient method, Proximal-ACCPM, to trigger the OBO approach and give a snapshot on numerical results. This paper summarizes several contributions with the OBO approach and aims to give, in a single report, enough information on the method and its implementation to facilitate new applications.
Research report, LOGILAB-HEC, University of Geneva, October 2004