Understanding logistic regression loss function equation I am writing a scientific paper that - among other things - deals with logistic regression in the context of machine learning.
I read this article where the author states that, given a set of instance-label pairs $(\boldsymbol{x_i},y_i),\  i=1,...,l\ \ \boldsymbol(x_i) \in R^n,\ y_i \in \{-1,+1\}$, Logistic Regression solves the following optimization problem:

$$
\begin{equation}\label{eq:log}
  \min_{w} \frac{1}{2}\boldsymbol{w}^T\boldsymbol{w} + C\sum\limits_{i=1}^l log(1+e^{-y_i\boldsymbol{w}^T \boldsymbol{x_i}})
\end{equation}\ \ \ \ \ \ \ \ \ \  (Eq.1)
$$

Is it correct if I say that: "The first summand of Equation 1 is a regularization term while the second represents the negative log-likelihood loss function"?

Thank you for your kind assistance.
Yes the first is the L2 regularization term to keep the norm of weights parameter as small as possible.