A path following interior-point algorithm for semidefinite optimization problem based on new kernel function

Abstract

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a 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 $O(6(m+1)^{frac{3m+4}{2(m+1)}}Psi _{0}^{frac{m+2}{2(m+1)}}frac{1}{theta }log frac{nmu ^{0}}{varepsilon })$, where $m>4$.