We present some characterizations of the ordered weighted \(\ell _1\) norm (aka sorted \(\ell _1\) norm) and of the vector Ky-Fan norm as solutions to linear programs involving reasonably many variables and constraints. Such linear characterizations can be exploited to recast and effortlessly solve a variety of convex optimization problems involving these norms. Similar linear characterizations are given for the dual norms of the ordered weighted \(\ell _1\) norm and the Ky-Fan norm.

中文翻译：

---

促进OWL规范的最小化

我们介绍了有序加权\（\ ell _1 \）范数（又名排序的\（\ ell _1 \）范数）和矢量Ky-Fan范数的一些刻画，作为涉及合理变量和约束的线性程序的解。可以利用这种线性表征来重铸并毫不费力地解决涉及这些准则的各种凸优化问题。对于有序加权\（\ ell _1 \）范数和Ky-Fan范数的对偶范数，给出了相似的线性特征。