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<p>The current portfolio optimization problem consistently exhibits a group-sparse structure due to similarities within an industry. In this paper, we consider a group-sparse portfolio selection (GSPSO) problem. By decomposing the difference of two convex functions, we formulate an exact penalty method for GSPSO, where the group-sparsity constraint is enforced via a regularizer. In particular, we provide an explicit estimate for the penalty parameter in the long-only case. Consequently, we develop an efficient algorithm based on proximal difference-of-convex (DC) methodology. We prove that the proximal DC method converges to an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\epsilon\)</EquationSource> </InlineEquation>-approximate first-order stationary point of the penalized problem. Numerical experiments on real-world data demonstrate that the proposed method can identify key sectors and generate a sparse portfolio. Moreover, our model achieves superior out-of-sample performance compared to benchmark portfolio strategies.</p>

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An exact penalty method for group-sparse portfolio selection

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Hongxin Zhao,
  • Xin Wang,
  • Hou-Duo Qi,
  • Lingchen Kong

摘要

The current portfolio optimization problem consistently exhibits a group-sparse structure due to similarities within an industry. In this paper, we consider a group-sparse portfolio selection (GSPSO) problem. By decomposing the difference of two convex functions, we formulate an exact penalty method for GSPSO, where the group-sparsity constraint is enforced via a regularizer. In particular, we provide an explicit estimate for the penalty parameter in the long-only case. Consequently, we develop an efficient algorithm based on proximal difference-of-convex (DC) methodology. We prove that the proximal DC method converges to an \(\epsilon\) -approximate first-order stationary point of the penalized problem. Numerical experiments on real-world data demonstrate that the proposed method can identify key sectors and generate a sparse portfolio. Moreover, our model achieves superior out-of-sample performance compared to benchmark portfolio strategies.