论文标题
计算$ \ ell_1 $诱导矩阵规范的近端运算符
Computing the proximal operator of the $\ell_1$ induced matrix norm
论文作者
论文摘要
在这篇简短文章中，对于任何矩阵$ x \ in \ mathbb {r}^{n \ times m} $是两个诱导标准的接近操作员$ \ | x \ | _1 $和$ \ | x \ | x \ | _ {\ | _ {\ infty} $。尽管没有获得密切的表达式，但描述了一个算法过程，该过程大致花费了$ \ Mathcal {o}（nm）$。该算法依赖于从Karush-Kuhn-Tucker条件得出的真实参数的一分点，遵循Parikh（2014）中$ \ Max $函数的近端运算符的证明思想。
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 $\mathcal{O}(nm)$. 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).
