Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are for small-update methods and for large-update, respectively. The resulting bound is better than the classical kernel function. For small-update, the iteration complexity is the best known bound for such methods.