I'm reading a paper that (vaguely) states that the following problem is an SOCP:
\begin{equation*} \begin{aligned} \max& \hspace{0.4cm} f(x_{0},x_{1},\cdots,x_{2n}) \\ \text{subject to}& \hspace{0.4cm} g(x_{0},x_{1},\cdots,x_{2n}) = 0 \\ \text{and}& \hspace{0.4cm} \sqrt{\sum_{i=0}^{n} x_{i}^{2}} + \sqrt{\sum_{i=n+1}^{2n} x_{i}^{2}} \leq 1, \end{aligned} \end{equation*} where $f$ and $g$ are linear functions. How can this last constraint be interpreted such that it's obvious this problem is an SOCP?
Introduce nonnegative variables $y$ and $z$ to represent the square roots, and impose \begin{align} y + z &\le 1 \\ y^2 &\ge \sum_{i=0}^n x_i^2 \\ z^2 &\ge \sum_{i=n+1}^{2n} x_i^2 \end{align}