Polynomial Variable Metric Methods For Linear Optimization

Abstract

Since the elaboration of the framework by Karmarkar, many interior point algorithms have been proposed for linear optimization. Although these variants can be classified into main categories, e.g.: (i) projective methods, (ii) “pure” affine-scaling methods, (iii) path-following methods, (iv) affine potential reduction methods, a different variant needs a different investigation of its convergence or polynomial status. Thus, there is a natural question: how should we analyze the behaviour of these algorithms? A good survey was published on interior point methods (Terlaky (ed.), 1996).