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<p>The nonlinear complementarity problems (NCPs) frequently arise in various fields, including engineering, management science, operations research, and scientific computing. This paper introduces a generalized accelerated overrelaxation method, in which one case reduces to the generalized successive overrelaxation method for solving NCPs. Additionally, the proposed method simplifies to a solver for linear complementarity problems. The primary objectives of the proposed methods are to enhance the convergence speed, reduce the number of iteration steps, and minimize memory usage when dealing large-scale problems. Furthermore, we discuss the convergence of the suggested techniques for an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2024_2334_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>H</mi> </math></EquationSource> </InlineEquation><b>-</b>matrix (strictly diagonally dominant or irreducible). Numerical experiments validate the applicability and efficiency of our methods.</p>

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Numerical exploration of two generalized iteration methods for solving nonlinear complementarity problems

  • 期刊论文

  • 发表日期：

    2025年1月10日

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  • Dawood Hussain,
  • Kejia Pan,
  • Bharat Kumar

摘要

The nonlinear complementarity problems (NCPs) frequently arise in various fields, including engineering, management science, operations research, and scientific computing. This paper introduces a generalized accelerated overrelaxation method, in which one case reduces to the generalized successive overrelaxation method for solving NCPs. Additionally, the proposed method simplifies to a solver for linear complementarity problems. The primary objectives of the proposed methods are to enhance the convergence speed, reduce the number of iteration steps, and minimize memory usage when dealing large-scale problems. Furthermore, we discuss the convergence of the suggested techniques for an \(H\) H -matrix (strictly diagonally dominant or irreducible). Numerical experiments validate the applicability and efficiency of our methods.