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<p>This paper aims to find a sparse solution for the linear complementarity problem (LCP) by solving a composite optimization problem with nonnegative constraint. We propose nonnegative proximal gradient algorithm with extrapolation technique, after illustrating the relationship between the nonnegative proximal operator and the standard one. We present the convergence of our proposed algorithm to a stationary point of the composite optimization problem. Furthermore, we establish the approximate global convergence of proposed algorithm for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> regularization problem as a special case. Numerical results demonstrate the effectiveness of proposed algorithm in approaching a sparse solution for the LCP. Finally, the application to Markowitz portfolio selection is discussed.</p>

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Accelerated nonnegative proximal gradient algorithm for sparse linear complementarity problem

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Xinlin Hu,
  • Kai Zhang

摘要

This paper aims to find a sparse solution for the linear complementarity problem (LCP) by solving a composite optimization problem with nonnegative constraint. We propose nonnegative proximal gradient algorithm with extrapolation technique, after illustrating the relationship between the nonnegative proximal operator and the standard one. We present the convergence of our proposed algorithm to a stationary point of the composite optimization problem. Furthermore, we establish the approximate global convergence of proposed algorithm for the \(\ell _0\) ℓ 0 regularization problem as a special case. Numerical results demonstrate the effectiveness of proposed algorithm in approaching a sparse solution for the LCP. Finally, the application to Markowitz portfolio selection is discussed.