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<p>Penalized support vector machines are effective tools for efficiently classifying high-dimensional data. Despite their advantages, the non-smooth nature of the hinge loss function poses considerable challenges to designing efficient optimization algorithms. To close this gap, we propose a convolution-based smoothing approach that effectively addresses the non-smoothness issue while preserving convexity. The improved smoothness and retained convexity facilitate the construction of a proximal gradient descent algorithm. Comprehensive numerical experiments conducted on both simulated and real-world datasets highlight the superior performance of the proposed methods compared to existing algorithms.</p>

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A unified and efficient proximal gradient descent algorithm for penalized convoluted support vector machines

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月20日

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  • Bingzhen Chen,
  • Canyi Chen

摘要

Penalized support vector machines are effective tools for efficiently classifying high-dimensional data. Despite their advantages, the non-smooth nature of the hinge loss function poses considerable challenges to designing efficient optimization algorithms. To close this gap, we propose a convolution-based smoothing approach that effectively addresses the non-smoothness issue while preserving convexity. The improved smoothness and retained convexity facilitate the construction of a proximal gradient descent algorithm. Comprehensive numerical experiments conducted on both simulated and real-world datasets highlight the superior performance of the proposed methods compared to existing algorithms.