A new corrector–predictor interior-point method for symmetric cone optimization

In this work, we present a corrector–predictor interior-point method for symmetric cone optimization based on Euclidean Jordan algebras as a key tool. Indeed, we extend Darvay et al.’s original technique introduced in (Cent Eur J Oper Res 28(3):1123–1140, 2020) for linear optimization to symmetric cone optimization. An algebraic equivalent transformation of the system defining the central path, based on the function ψ(t)=t-t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi (t)=t-\sqrt{t}$$\end{document}, is used to obtain the search directions. At each iteration, the algorithm takes a damped Nesterov–Todd step in the predictor stage and a full Nesterov–Todd step in the corrector stage. We discuss the global convergence analysis of the proposed algorithm and prove that the complexity bound coincides with the one obtained for linear optimization. Moreover, numerical results show the efficiency of the proposed method.