Ghami, A class of large-update and small-update primaldual interior-point algorithms for linear optimization

Abstract In this paper we present a class of polynomial primal-dual interior-point al-gorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the classical logarithmic function, the prototype self-regular function, and non-self-regular kernel functions as special cases. The analy-sis of the algorithms in the paper follows the same line of arguments as in Bai et al. (SIAM J. Optim. 15:101–128, 2004), where a variety of non-self-regular kernel functions were considered including the ones with linear and quadratic growth terms. However, the important case when the growth term is between linear and quadratic was not considered. The goal of this paper is to introduce such class of kernel func-tions and to show that the interior-point methods based on these functions have fa-vorable complexity results. They match the currently best known iteration bounds for the prototype self-regular function with quadratic growth term, the simple non-self-regular function with linear growth term, and the classical logarithmic kerne