On complexity analysis of the primal–dual interior-point method for semidefinite optimization problem based on a new proximity function Original Research Article

The purpose of this paper is to obtain new complexity results for a semidefinite optimization (SDO) problem. We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a large-update primal–dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is View the MathML sourceO(n(logn)q+1qlognϵ), where q≧1q≧1.