Abstract
In this paper, we consider a full-Newton step feasible interior-point algorithm for \(P_*(\kappa )\)-linear complementarity problem. The perturbed complementarity equation \(xs=\mu e\) is transformed by using a strictly increasing function, i.e., replacing \(xs=\mu e\) by \(\psi (xs)=\psi (\mu e)\) with \(\psi (t)=\sqrt{t}\), and the proposed interior-point algorithm is based on that algebraic equivalent transformation. Furthermore, we establish the currently best known iteration bound for \(P_*(\kappa )\)-linear complementarity problem, namely, \(O((1+4\kappa )\sqrt{n}\log \frac{n}{\varepsilon })\), which almost coincides with the bound derived for linear optimization, except that the iteration bound in the \(P_{*}(\kappa )\)-linear complementarity problem case is multiplied with the factor \((1+4\kappa )\).
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Acknowledgments
The authors would like to thank the Editor and the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper. This work was supported by National Natural Science Foundation of China (Nos. 11471211, 11371253), Shanghai Natural Science Fund Project (No. 14ZR1418900), China Postdoctoral Science Foundation funded project (No. 2012T50427) and Natural Science Foundation of Shanghai University of Engineering Science (No. 2014YYYF01).
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Wang, G.Q., Fan, X.J., Zhu, D.T. et al. New complexity analysis of a full-Newton step feasible interior-point algorithm for \(P_*(\kappa )\)-LCP. Optim Lett 9, 1105–1119 (2015). https://doi.org/10.1007/s11590-014-0800-4
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DOI: https://doi.org/10.1007/s11590-014-0800-4