I am looking for an explicit description and discussion of the dual of the $\ell^1$-norm minimization problem $\lVert A x\rVert_1\to\min$, where $A$ is a matrix, and $x$ belongs to the $n$-simplex $\sum_{i=0}^n x_i =1, x_i\ge 0$.
EDIT Apparently those who voted for closing this question had hard time recognizing the "reference request" tag. I do know how to reformulate this as a linear programming problem and how to construct the dual problem. The question is about references to works where this was done in the particular situation described in the question.