Complexity analysis of infeasible interior-point method for semidefinite optimization based on a new trigonometric kernel function

Abstract

In this paper, a full Nesterov–Todd step infeasible interior-point method for solving semidefinite optimization problems based on a new kernel function is analyzed. In each iteration, the algorithm involves a feasibility step and several centrality steps. The centrality step is focused on Nesterov–Todd search directions, while we used a kernel function with trigonometric barrier term to induce the feasibility step. The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.