# How Vectorize the Objective of Sum of ${L}_{1}$ Norms

I would like to write the following objective for CVX:

$$\arg \min_{x} \sum_{i = 1}^{m} {\left| x - {y}{i} \right|}{1}$$

Where x \in \mathbb{R}^{n} .

Namely, we are after the {L}_{1} minimizer of the set of vectors {\left\{ {y}_{i} \right\}}_{i = 1}^{m} .

I can write the loop in CVX yet I wonder if there is a vectorized way to write it.

I thought about something like {\left\| Y - x \boldsymbol{1}^{T} \right\|}_{1, 1} then use norms(). Yet I wonder if there a way to return to a vector norm using some vecotrization tricks.

What is wrong with using sum(norms(...)) ?

Because I already did that as I wrote.
I am asking if there is a more vectorized manner to write it.

That seems vectorized to me. I doubt you’re going to do any better with anything else.