I need help interpreting an expression

Question

I have the following formula:

$$\min_{\beta_0,\beta}\sum_{i=1}^n[1-y_if(x_i)]_++\frac1{2C}\lVert \beta\rVert^2$$

What does the bracket with the subscripted plus mean?

I greatly appreciate your help. Thank you.

Answer 1

Quite often, $x_+$ indicates $\max\{x,0\}$ and $x_-$ indicates $-\min\{x,0\}=(-x)_+$. Under these conventions $$\lvert x\rvert=x_++x_-\\ x=x_+-x_-$$