A full-Newton step infeasible interior-point method for linear optimization based on a trigonometric kernel function

Abstract

An infeasible interior-point method (IIPM) for solving linear optimization problems based on a kernel function with trigonometric barrier term is analysed. In each iteration, the algorithm involves a feasibility step and several centring steps. The centring step is based on classical Newton’s direction, while we used a kernel function with trigonometric barrier term in the algorithm to induce the feasibility step. The complexity result coincides with the best-known iteration bound for IIPMs. To our knowledge, this is the first full-Newton step IIPM based on a kernel function with trigonometric barrier term.

Keywords:

• linear optimization
• infeasible interior-point method
• full-Newton step
• trigonometric kernel function

AMS Subject classification:

• 90C51

Acknowledgements

The authors are grateful to two anonymous referees and the editors for their constructive comments and suggestions to improve the presentation.

Notes

No potential conflict of interest was reported by the authors.