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<p>Complementarity problems are essential in various fields, including but not limited to scientific computing, engineering, operations research, and management science. In this paper, we introduce a novel three-step modulus-based matrix splitting (three-step MMS) method for solving nonlinear complementarity problems. The proposed method greatly speeds up convergence, reduces the number of required iterations, and minimizes error accumulation through spectral radius control. Through rigorous convergence analysis, we demonstrate the applicability and effectiveness of the three-step MMS method for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2238_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{+}\)</EquationSource> </InlineEquation>-matrices under less restrictive conditions. The efficiency of the proposed method is confirmed by numerical experiments, and its performance is compared with existing methods, especially showing strong effectiveness for large-scale problems. The proposed method can save about 20% of the time compared with the two-step method. The results highlight its potential for both theoretical advancements and practical applications in solving complementarity problems.</p>

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A three-step modulus-based iterative method for solving nonlinear complementarity problems

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Dawood Hussain,
  • Kejia Pan,
  • Ruiting Li,
  • You Li

摘要

Complementarity problems are essential in various fields, including but not limited to scientific computing, engineering, operations research, and management science. In this paper, we introduce a novel three-step modulus-based matrix splitting (three-step MMS) method for solving nonlinear complementarity problems. The proposed method greatly speeds up convergence, reduces the number of required iterations, and minimizes error accumulation through spectral radius control. Through rigorous convergence analysis, we demonstrate the applicability and effectiveness of the three-step MMS method for \(H_{+}\) -matrices under less restrictive conditions. The efficiency of the proposed method is confirmed by numerical experiments, and its performance is compared with existing methods, especially showing strong effectiveness for large-scale problems. The proposed method can save about 20% of the time compared with the two-step method. The results highlight its potential for both theoretical advancements and practical applications in solving complementarity problems.