Primal-dual interior point methods for semidefinite programming based on a new type of kernel functions

Abstract

In this paper, we first propose a new hyperbolic-logarithmic kernel function for Semidefinite programming problems. By simple analysis tools, several properties of this kernel function are used to compute the total number of iterations. We show that the worst-case iteration complexity of our algorithm for large-update methods improves the obtained iteration bounds based on hyperbolic \cite{touichi} as well as classic kernel functions.
For small-update methods, we derive the best known iteration bound.