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.