A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO

Kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not only used for determining the search directions but also for measuring the distance between the given iterate and the mu-center for the algorithms. In this paper we present a unified kernel function approach to primal-dual interior-point algorithms for convex quadratic semidefinite optimization based on the Nesterov and Todd symmetrization scheme. The iteration bounds for large- and small-update methods obtained are analogous to the linear optimization case. Moreover, this unifies the analysis for linear, convex quadratic and semidefinite optimizations.