An algorithm for solving the convex feasibility problem

This paper presents a volumetric cutting plane algorithm for finding a feasible point in a convex set. It is based on the volumetric barrier function where Newton steps are taken and a line search is performed in order to re-centre following the addition or deletion of a constraint. The placement of the separating hyperplane in relation to the volumetric center is discussed from a theoretic perspective and then further explored in the practical implementation of the algorithm. Promising values for the parameters that have the greatest influence on the performance of the algorithm are presented.