A full‐NT‐step infeasible interior‐point algorithm for SDP based on kernel functions

This paper proposes an infeasible interior‐point algorithm with full Nesterov–Todd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. First we present a full NT step infeasible interior‐point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introduced. The feasibility step is induced by this kernel function instead of the classic logarithmical barrier function. This kernel function has a finite value on the boundary. The result of polynomial complexity, $O(n\log n/ϵ)$ , coincides with the best known one for infeasible interior‐point methods.