Proximal Gradient Descent

Junwei Lu
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Junwei Lu: Harvard University

Chapter Chapter 14 in Big Data Analysis, 2025, pp 95-104 from Springer

Abstract: Abstract 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 β 1 2 ∥ Y − 𝕏 β ∥ 2 2 + λ ∥ β ∥ 1 $$\min _{\beta} \frac {1}{2}\|Y - \mathbb {X}\beta \|_2^2 + \lambda \|\beta \|_1$$ , the ℓ 1 $$\ell _1$$ -norm penalty term is not smooth.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-03161-7_14

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DOI: 10.1007/978-3-032-03161-7_14

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