New complexity analysis for primal-dual interior-point methods for self-scaled optimization problems

Abstract

A linear optimization problem over a symmetric cone, defined in a Euclidean Jordan algebra and called a self-scaled optimization problem (SOP), is considered. We formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOP by using a proximity function defined by a new kernel function, and we obtain the best known complexity results of the large-update IPM for the SOP by using the Euclidean Jordan algebra techniques. © 2012 Choi and Lee; licensee Springer.