Improved Complexity Analysis of Full Nesterov-Todd Step Feasible Interior-Point Method for Symmetric Optimization

Abstract

In this paper an improved complexity analysis of full Nesterov-Todd step feasible interior-point method for symmetric optimization is considered. Specifically we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore we derive the currently best known iteration bound for full Nesterov-Todd step feasible interior-point method.