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<p>In this paper, we propose to use geometrically smoothed momentum to accelerate the convergence rate of both the modulus-based matrix splitting iteration methods and the accelerated modulus-based matrix splitting iteration methods for solving linear complementarity problem. Convergence of the proposed methods is proved when the system matrix is a positive-definite matrix or an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_+\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mo>+</mo> </msub> </math></EquationSource> </InlineEquation>-matrix. We compare the performance of these methods with and without acceleration by geometrically smoothed momentum on two examples. The results demonstrate that modulus-based iteration methods with geometrically smoothed momentum acceleration converge much more rapidly than those without it.</p>

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Acceleration of the modulus-based iteration methods for solving linear complementarity problems by momentum

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Yong Liu,
  • Jian-Jun Zhang

摘要

In this paper, we propose to use geometrically smoothed momentum to accelerate the convergence rate of both the modulus-based matrix splitting iteration methods and the accelerated modulus-based matrix splitting iteration methods for solving linear complementarity problem. Convergence of the proposed methods is proved when the system matrix is a positive-definite matrix or an \(H_+\) H + -matrix. We compare the performance of these methods with and without acceleration by geometrically smoothed momentum on two examples. The results demonstrate that modulus-based iteration methods with geometrically smoothed momentum acceleration converge much more rapidly than those without it.