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<p>Machine learning algorithms have been recently applied to portfolio selection problems due to their simplicity of implementation and solution efficiency. This paper introduces one type of such algorithms known as the proximal distance algorithm (PDA) for the sparsity-constrained portfolio optimization, which is challenging for many existing algorithms. While PDA enjoys nice convergence properties, we focus on the issue how the penalty parameter would influence the solution quality. In particular, we study the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40305_2025_594_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-optimality of the penalized problem and establish an exact penalty result for the long-only sparse portfolio under certain conditions. We further introduce a new variant of PDA that is based on the exact penalization making use of the distance function to the sparsity set. We circumvent the nondifferentiability issue of the distance function by applying the majorization-minimization technique to develop the corresponding PDA. We also report extensive numerical results to validate the efficiency of the introduced PDAs. Specifically, the proposed portfolios demonstrate the superior out-of-sample performance by comparing with several state-of-the-art portfolio strategies.</p>

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Proximal Distance Algorithms for Sparse Portfolio Selections

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Hong-Xin Zhao,
  • Xin Wang,
  • Ling-Chen Kong

摘要

Machine learning algorithms have been recently applied to portfolio selection problems due to their simplicity of implementation and solution efficiency. This paper introduces one type of such algorithms known as the proximal distance algorithm (PDA) for the sparsity-constrained portfolio optimization, which is challenging for many existing algorithms. While PDA enjoys nice convergence properties, we focus on the issue how the penalty parameter would influence the solution quality. In particular, we study the \(\varepsilon \) ε -optimality of the penalized problem and establish an exact penalty result for the long-only sparse portfolio under certain conditions. We further introduce a new variant of PDA that is based on the exact penalization making use of the distance function to the sparsity set. We circumvent the nondifferentiability issue of the distance function by applying the majorization-minimization technique to develop the corresponding PDA. We also report extensive numerical results to validate the efficiency of the introduced PDAs. Specifically, the proposed portfolios demonstrate the superior out-of-sample performance by comparing with several state-of-the-art portfolio strategies.