A New Infeasible Interior-Point Method Based on a Non-Coercive Kernel Function with Improved Centering Steps for Second-Order Cone Optimization

Abstract

In this article, we present a new full Nesterov-Todd step infeasible interior-point method for second-order cone optimization based on a non-coercive kernel function. The main iteration consists of a so-called feasibility step and one centering step, whereas the earlier versions, in [4,21], needed two additional centering steps. We use a kernel function to induce the feasibility step. The new algorithm reduces the searching steps in each iteration and tenders an interesting analysis for complexity bound.