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

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.