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A Generic Interior-point Algorithm for Monotone Symmetric Cone Linear Complementarity Problems Based on a New Kernel Function

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

Kernel functions play an important role in defining new search directions for interior-point algorithms for solving monotone linear complementarity problems. In this paper we present a new kernel function which yields the complexity bounds \({\mathcal O}(\sqrt{r}\log r\log\frac{r}{\epsilon})\) and \({\mathcal O}(\sqrt{r}\log\frac{r}{\epsilon})\) for large-and small-update methods, respectively, which are currently the best known bounds for such methods.

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Authors and Affiliations

  1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Behrouz Kheirfam

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  1. Behrouz Kheirfam
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Correspondence to Behrouz Kheirfam.

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Kheirfam, B. A Generic Interior-point Algorithm for Monotone Symmetric Cone Linear Complementarity Problems Based on a New Kernel Function. J Math Model Algor 13, 471–491 (2014). https://doi.org/10.1007/s10852-013-9240-x

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  • DOI: https://doi.org/10.1007/s10852-013-9240-x

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