A Comparative Study of Kernel Functions for Primal-Dual Interior-Point Algorithms in Semidefinite Programming

Recently, Y. Q. Bai, M. El Ghami, and C. Roos introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interior-point methods for Linear Optimization based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the Semidefinite Optimization problem and we generalize the apprpach, as presented for linear optimization, to the semidefinite case. The iteration bounds obtained are analogous to the results for Linear Optimization.