NEW COMPLEXITY ANALYSIS OF INTERIOR POINT METHODS FOR SEMIDEFINITE OPTIMIZATION BASED ON A KERNEL FUNCTION WITH A TRIGONOMETRIC BARRIER TERM

Recently M. El Ghami et al. [1] introduced a new barrier function for primal-dual interior point methods in linear optimization which has a trigonometric barrier term. In this paper we extend the approach for LO based this new kernel function to SDO. We derive the complexity analysis for algorithms based on this kernel function, both with large and small-updates. The favorable complexity results are as good as those in the linear case.