I'm doing some self-study and came across this paper where it appears in Section 4 the authors are adding a scalar to the vector $\boldsymbol 1_{x\geq 0}$. The other two functions called $f$ are $\min_{\boldsymbol x} -\frac12 \boldsymbol x^T \Big ( \sum_{i=1}^n \boldsymbol z_i \boldsymbol z_i^T \Big ) \boldsymbol x + \gamma \|\boldsymbol x\|^2$. And this function $f$ is added to $g$, which is the indicator function $\boldsymbol 1_{x\geq 0}$.
In other word, it's unclear to me how this result is a scalar
$$ \min_{\boldsymbol x} -\frac12 \boldsymbol x^T \Big ( \sum_{i=1}^n \boldsymbol z_i \boldsymbol z_i^T \Big ) \boldsymbol x + \gamma \|\boldsymbol x\|^2 + \boldsymbol 1_{x\geq 0} $$
I'm pretty sure I'm the one in error here since they've gone ahead to declare results in the paper. I'm just curious how $g$ could be added to $f$ and still produce a scalar value $f+g$.
Can anyone explain this to me?
Thanks.
The $\boldsymbol 1_{x\geq 0}$ is in the $\min_x$ so that it's a scalar : $1$ if $x\ge 0$ and $0$ otherwise.