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Pré-Publication, Document De Travail Année : 2020

Computing the proximal operator of the $\ell_1$ induced matrix norm

Résumé

In this short article, for any matrix $X\in\mathbb{R}^{n\times m}$ the proximity operator of two induced norms $ \|X\|_1 $ and $ \|X\|_{\infty}$ are derived. Although no close form expression is obtained, an algorithmic procedure is described which costs roughly $\mathcal{O}(nm\log_2(n))$. This algorithm relies on a bisection on a real parameter derived from the Karush-Kuhn-Tucker conditions, following the proof idea of the proximal operator of the $ \max $ function found in Parikh(2014).

Dates et versions

hal-03037844 , version 1 (03-12-2020)

Identifiants

Citer

Jérémy E Cohen. Computing the proximal operator of the $\ell_1$ induced matrix norm. 2020. ⟨hal-03037844⟩
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