A New Primal-Dual Interior-Point Algorithm for Convex Quadratic Symmetric Cone Optimization Based on a Parametric Kernel Function

Abstract

In this paper, we present a class of primal-dual interior-point algorithms for convex quadratic symmetric cone optimization based on a parametric kernel function, which has been introduced for linear optimization. By using Euclidean Jordan algebras, we derive the iteration bounds that match the currently best known iteration bounds for large- and small-update methods, which are as good as the linear optimization analogue.