Primal-dual algorithms for semidifinite optimization problems based on Kernel-function with trigonometric barrier term

In this paper we extended the results obtained for the first trigonometric kernel-function-based IPMs introduced by El Ghami et al. in [8] for LO to semidefinite optimization problems. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.