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In the previous chapter, we introduce the gradient descent and accelerated gradient algorithm to solve the unconstrained optimization. We show the convergence rates of these two algorithms when the objective function is smooth. However, in Lasso \(\min _{\beta } \frac {1}{2}\|Y - \mathbb {X}\beta \|_2^2 + \lambda \|\beta \|_1\) , the \(\ell _1\) -norm penalty term is not smooth.

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Proximal Gradient Descent

  • 章节

  • 发表日期：

    2025年

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  • Junwei Lu

摘要

In the previous chapter, we introduce the gradient descent and accelerated gradient algorithm to solve the unconstrained optimization. We show the convergence rates of these two algorithms when the objective function is smooth. However, in Lasso \(\min _{\beta } \frac {1}{2}\|Y - \mathbb {X}\beta \|_2^2 + \lambda \|\beta \|_1\) , the \(\ell _1\) -norm penalty term is not smooth.