Sum of the largest components
= Sum of the largest components
The sum of the $k$ largest components of $x\in\mathbb R^n$ is the <support function> of the <capped simplex>: $\sum_{i=1}^k x_{[i]}=\max\{x^Tv:0\leq v\leq1,\ \sum_i v_i=k\}$.
= Sum of the largest components
The sum of the $k$ largest components of $x\in\mathbb R^n$ is the <support function> of the <capped simplex>: $\sum_{i=1}^k x_{[i]}=\max\{x^Tv:0\leq v\leq1,\ \sum_i v_i=k\}$.