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An infeasible interior-point algorithm with full-Newton steps for \(P_*(\kappa )\) horizontal linear complementarity problems based on a kernel function

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Abstract

This paper contains an infeasible interior-point method for \(P_*(\kappa )\) horizontal linear complementarity problem based on a kernel function. The kernel function is used to determine the search directions. These search directions differ from the usually used ones in some interior-point methods, and their analysis is more complicated. Main feature of our algorithm is that there is no calculation of the step size, i.e, we use full-Newton steps at each iteration. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem, close to its central path. Two types of full-Newton steps are used, feasibility steps and centering steps. The iteration bound matches the best-known iteration bound for these types of algorithms.

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Acknowledgments

Authors would like to thank for the financial grant from Shahrekord University. They were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    S. Asadi, M. Zangiabadi & H. Mansouri

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  1. S. Asadi
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  2. M. Zangiabadi
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  3. H. Mansouri
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Correspondence to M. Zangiabadi.

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Asadi, S., Zangiabadi, M. & Mansouri, H. An infeasible interior-point algorithm with full-Newton steps for \(P_*(\kappa )\) horizontal linear complementarity problems based on a kernel function. J. Appl. Math. Comput. 50, 15–37 (2016). https://doi.org/10.1007/s12190-014-0856-4

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  • DOI: https://doi.org/10.1007/s12190-014-0856-4

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