A full Nesterov–Todd step infeasible-interior-point algorithm for Cartesian P_*(κ) horizontal linear complementarity problems over symmetric cones

Abstract

Euclidean Jordan algebra is a commonly used tool in designing interior-point algorithms for symmetric cone programs. In this paper, we present a full Nesterov–Todd (NT) step infeasible interior-point algorithm for horizontal linear complementarity problems over Cartesian product of symmetric cones. Since the algorithm uses only full-NT feasibility and centring steps, it has the advantage that no line searches are needed. The complexity result obtained here for symmetric cones using NT directions coincides with the best bound obtained for horizontal linear complementarity problems.

Keywords:

• interior-point methods
• horizontal linear complementarity problems
• Euclidean Jordan algebras
• symmetric cones

Acknowledgements

The authors would like to thank the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors also wish to thank Shahrekord University for financial support. The authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.