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(nlogn/ε)O(nlogn/ε), coincides with the best known one for infeasible interior-point methods.