# What is the name of the 1/2 sum of square errors function?

What is the name of this function:

$E = \frac{1}{2}\ \sum\limits_{n=1}^N \{ output_n - target_n\}^2$

Which is used in machine learning (e.g. error back prop).

I have sometimes seen the name "MSE" for this, but there is nothing "Mean" here because MSE is calculated differently,

Without the $\frac{1}{2}$, it's the residual sum of squares.
If your aim is minimization of MSE, you can minimize any strictly monotone function $g$ of MSE, e.g. $$E := g(\text{MSE}) = n \text{MSE}/2.$$