# Lipschitz constant of L2 reg. logistic regression $\sum_i \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2$

Let the L2 regularized logistic regression function is given by, \begin{align} f(w) &= \frac{1}{N} \sum_i \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2 \ = \frac{1}{N} \sum_i f_i(w), \end{align} where $$t_i \in \mathbb{R}$$, $$w, x_i \in \mathbb{R}^n$$, $$\mu \in \mathbb{R}$$, and $$f_i(w) := \log \left(1 + \exp\left\{ -t_i \left(w^T x_i\right)\right\} \right) + \mu \|w \|_2^2$$ .

Questions:

• How would/could I find the (small) Lipschitz constant $$M$$ and $$\nu$$-strongly parameter of $$f(w)$$?
• How can I find the (small) Lipschitz constant $$L$$ of $$\nabla f(w)$$ and $$L_i$$ of $$\nabla f_i(w)$$?

I am sorry if this question has already been asked or it is trivial to compute (analytically?).