A predictor-corrector infeasible-interior-point method for the Cartesian -LCP over symmetric cones with iteration complexity

Abstract

In this paper, we present a predictor-corrector infeasible-interior-point method for symmetric cone linear complementarity problem (SCLCP) with the Cartesian -property (-SCLCP). This method is based on a wide neighbourhood, which is an even wider neighbourhood than the negative infinity neighbourhood. We show that the iteration-complexity bound of the proposed algorithm for a commutative class of search directions is , where is the condition number of matrix G, is the handicap of the problem, r is the rank of the associated Euclidean Jordan algebra and is a given tolerance. To our knowledge, this is the best complexity result obtained so far for the wide neighbourhood infeasible-interior-point methods for the Cartesian -SCLCPs.

Keywords:

• Infeasible-interior-point method
• wide neighborhood
• linear complementarity problem
• symmetric cone programming
• -property

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. The authors would like 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. The second and third authors wish to thank the York University, Professor Michael Chen and his group for hospitality during their recent sabbatical.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shahrekord University [grant numbers 94GRD1M2003, 94GRD1M1034].