A Long-Step Primal-Dual Algorithm for the Symmetric Programming Problem

Based on the techniques of Euclidean Jordan algebras, we prove complexity estimates for a long-step primal-dual interior-point algorithm for the optimization problem of the minimization of a linear function on a feasible set obtained as the intersection of an ane subspace and a symmetric cone. This result provides a meaningful illustration of a power of the technique of Euclidean Jordan algebras applied to problems under consideration