A unified kernel function approach to primal‐dual interior‐point algorithms for convex quadratic SDO (semidefinite optimization)

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 μ‐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.