A full-Newton step feasible interior-point algorithm for P*(κ)-linear complementarity problems

Authors:
G. Q. Wang;C. J. Yu;K. L. Teo
Affiliations:
College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, People's Republic of China 201620;Department of Mathematics and Statistics, Curtin University, Perth, Australia 6845;Department of Mathematics and Statistics, Curtin University, Perth, Australia 6845
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving $$P_*(\kappa )$$ P 驴 ( 驴 ) -linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, $$O\left( (1+4\kappa )\sqrt{n}\log {\frac{n}{\varepsilon }}\right) $$ O ( 1 + 4 驴 ) n log n 驴 , which matches the currently best known iteration bound for $$P_*(\kappa )$$ P 驴 ( 驴 ) -linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.