Abstract
In this paper, we propose an infeasible interior-point algorithm for linear complementarity problems. In every iteration, the algorithm constructs an ellipse and searches an \(\varepsilon \)-approximate solution of the problem along the ellipsoidal approximation of the central path. The theoretical iteration-complexity of the algorithm is derived and the algorithm is proved to be polynomial with the complexity bound \(O\left(n\log \varepsilon ^{-1}\right)\) which coincides with the best known iteration bound for infeasible interior-point methods.
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Acknowledgments
The authors thank the anonymous referees for their useful comments and suggestions, which helped us in improving the presentation of the manuscript. The authors also thank Shahrekord University for the financial support. The authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.
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Pirhaji, M., Zangiabadi, M. & Mansouri, H. An \(\ell _{2}\)-neighborhood infeasible interior-point algorithm for linear complementarity problems. 4OR-Q J Oper Res 15, 111–131 (2017). https://doi.org/10.1007/s10288-016-0325-z
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DOI: https://doi.org/10.1007/s10288-016-0325-z