A new full Nesterov–Todd step feasible interior-point method for convex quadratic symmetric cone optimization

Abstract

In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, O(rlogrε). Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.