Research Article: On Extending Primal-Dual Interior-Point Method for Linear Optimization to Convex Quadratic Symmetric Cone Optimization

Abstract

In this article, we generalize primal-dual interior-point method, which was studied by Bai et al. [3] for linear optimization, to convex quadratic optimization over symmetric cone. The symmetrization of the search directions used in this article is based on the Nesterov and Todd scaling scheme. By employing Euclidean Jordan algebras, we derive the iteration bounds that match the currently best known iteration bounds for large- and small-update methods, namely, and , respectively, which are as good as the ones for the linear optimization analogue. Moreover, this unifies the analysis for linear optimization, convex quadratic optimization, second-order cone optimization, semidefinite optimization, convex quadratic semidefinite optimization, and symmetric optimization.