The lp regression problem takes as input a matrix $A \in \Real^{n \times d}$,
a vector $b \in \Real^n$, and a number $p \in [1,\infty)$, and it returns as
output a number ${\cal Z}$ and a vector $x_{opt} \in \Real^d$ such that ${\cal
Z} = \min_{x \in \Real^d} ||Ax -b||_p = ||Ax_{opt}-b