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<p>In this paper, a new method for solving the vertical linear complementarity problems is established by the nonsmooth Newton iteration. With the row <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11590_2024_2182_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {W}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">W</mi> </math></EquationSource> </InlineEquation>-property of the set of the system matrices, the nonsingularity of the generalized Jacobian is proved and the nearly one-step convergence is presented. Furthermore, a hybrid nonsmooth Newton method is constructed to obtain global convergence. Finally, numerical examples are given to demonstrate the efficiency of the proposed methods.</p>

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Nonsmooth Newton methods for vertical linear complementarity problems

  • 期刊论文

  • 发表日期：

    2025年1月9日

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  • Hua Zheng,
  • Xiaoping Lu,
  • Seakweng Vong

摘要

In this paper, a new method for solving the vertical linear complementarity problems is established by the nonsmooth Newton iteration. With the row \(\mathcal {W}\) W -property of the set of the system matrices, the nonsingularity of the generalized Jacobian is proved and the nearly one-step convergence is presented. Furthermore, a hybrid nonsmooth Newton method is constructed to obtain global convergence. Finally, numerical examples are given to demonstrate the efficiency of the proposed methods.