A wide neighborhood infeasible-interior-point method with arc-search for -SCLCPs

Abstract

In this paper, we propose an arc-search infeasible-interior-point method based on the wide neighbourhood for linear complementarity problems over symmetric cones with the Cartesian -property (-SCLCP). The algorithm searches the optimizers along the ellipses that approximate the central path. Moreover, we derive the complexity bound of the algorithm which coincides with the currently best known theoretical complexity bounds for the short step path-following algorithm. Some numerical results are provided to demonstrate the computational performance of the proposed algorithm.

Keywords:

• Interior-point method
• symmetric cone
• Euclidean Jordan algebra
• arc-search directions

Acknowledgements

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

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the first author was in part supported by a grant from IPM [grant number 96900076]. The second and third authors would like to thank Shahrekord University for financial support [grant number 94GRD1M2003], [grant number 94GRD1M1034]. The second and third authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.