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Abstract <p>In this paper, we propose two new classes of kernel functions (KFs) with hyperbolic barrier terms and define interior-point methods (IPMs) based on these functions to solve linear complementarity problems (LCPs). The two proposed classes have similar forms but are different. One of them is a generalization, up to a multiplicative constant, to the KF recently introduced by Guerdouh et al. (J.&#xa0;Appl. Math. Comput. 1–19 (2023)). According to our analysis, the worst-case iteration complexity of large-update IPMs enjoys the best iteration bound <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2243_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="130" /> </InlineMediaObject> <EquationSource Format="TEX">\(O\left( {\sqrt n \log n\log \frac{n}{\epsilon }} \right)\)</EquationSource> <!--ComMat2570054Bouhenache-m1--> </InlineEquation> for large-update methods with special choices of the parameters. This bound coincides with the so far best known complexity results obtained from KFs for LCPs. Finally, some numerical issues regarding the practical performance of the new proposed KFs are reported.</p>

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An Interior-Point Algorithm for LCP Based on a Parameterized Hyperbolic Kernel Function

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Y. Bouhenache,
  • W. Chikouche,
  • S. Guerdouh

摘要

Abstract

In this paper, we propose two new classes of kernel functions (KFs) with hyperbolic barrier terms and define interior-point methods (IPMs) based on these functions to solve linear complementarity problems (LCPs). The two proposed classes have similar forms but are different. One of them is a generalization, up to a multiplicative constant, to the KF recently introduced by Guerdouh et al. (J. Appl. Math. Comput. 1–19 (2023)). According to our analysis, the worst-case iteration complexity of large-update IPMs enjoys the best iteration bound \(O\left( {\sqrt n \log n\log \frac{n}{\epsilon }} \right)\) for large-update methods with special choices of the parameters. This bound coincides with the so far best known complexity results obtained from KFs for LCPs. Finally, some numerical issues regarding the practical performance of the new proposed KFs are reported.