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.

Keywords:

• Full Nesterov-Todd step
• Infeasible interior-point method
• Polynomial complexity
• Second-order cone optimization

2000 Mathematics Subject Classification:

• 90C51
• 90C25