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<p>With the definition of modulus on the second-order cone, we present a new equivalent formulation for the implicit complementarity problem over second-order cone (abbreviated as ICP-SOC). Crucially departing from existing literature, our formulation eliminates auxiliary variable requirements. Building upon this foundation, we develop a class of modulus-based matrix splitting methods specifically designed for ICP-SOC. Sufficient convergence conditions for the proposed methods are rigorously derived. Numerical experiments demonstrate significant computational efficiency improvements over established benchmark techniques.</p>

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A new modulus-based approach for solving implicit complementarity problem over second-order cone

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Shuhong Wen,
  • Yifen Ke,
  • Xiwen Chen,
  • Lifen Xiao

摘要

With the definition of modulus on the second-order cone, we present a new equivalent formulation for the implicit complementarity problem over second-order cone (abbreviated as ICP-SOC). Crucially departing from existing literature, our formulation eliminates auxiliary variable requirements. Building upon this foundation, we develop a class of modulus-based matrix splitting methods specifically designed for ICP-SOC. Sufficient convergence conditions for the proposed methods are rigorously derived. Numerical experiments demonstrate significant computational efficiency improvements over established benchmark techniques.