论文标题
计算稀疏投影到盒子中
Computing a Sparse Projection into a Box
论文作者
论文摘要
我们描述了一个程序，以计算$ w \ in \ mathbb {r}^n $的投影到所谓的\ emph {zero-norm}球$ k \ mathbb {b} _0 $ radius $ k $的交点\ Mathbb {B} _0 $。对这种投影的需求是在某些信任区域方法的上下文中出现的。尽管我们希望投影的集合是NonConvex，但我们表明可以在$ O（n \ log（n））$操作中找到解决方案。我们描述了我们的朱莉娅实施，并在两种信任区域方法的上下文中说明了我们的程序，以非平滑正规化优化。
We describe a procedure to compute a projection of $w \in \mathbb{R}^n$ into the intersection of the so-called \emph{zero-norm} ball $k \mathbb{B}_0$ of radius $k$, i.e., the set of $k$-sparse vectors, with a box centered at a point of $k \mathbb{B}_0$. The need for such projection arises in the context of certain trust-region methods for nonsmooth regularized optimization. Although the set into which we wish to project is nonconvex, we show that a solution may be found in $O(n \log(n))$ operations. We describe our Julia implementation and illustrate our procedure in the context of two trust-region methods for nonsmooth regularized optimization.
