# Computing the proximal operator of the ℓ1 induced matrix norm

arXiv: https://arxiv.org/abs/2005.06804 · HTML: https://mlsanity.com/paper/2005.06804/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2020.

## Built on by (most cited first, 1 of 1)

- [Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem](https://mlsanity.com/paper/2111.12399/) (2021)

## Abstract (arXiv)

In this short article, for any matrix X∈ℝn× m the proximity operator of two induced norms  |X|1  and  |X|∞ are derived. Although no close form expression is obtained, an algorithmic procedure is described which costs roughly O(nm). 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).