A primal–dual interior-point method for semidefinite optimization based on a class of trigonometric barrier functions

A primal–dual interior-point method (IPM) based on a new class of proximity functions is proposed for solving Semidefinite Optimization (SDO) problems. The proposed functions are induced from the kernel functions with trigonometric barrier terms. We derive iteration complexity of large-update IPMs for SDO as O(nlognlognϵ). This improves the result obtained in Li and Zhang (2015) for linear optimization and matches to the bound for the so-called self-regular kernel functions.