I'm trying to minimize the following:
$||Ax - b|| - c$
$A$ : $K \times M$ matrix
$x$ : $M \times N$ unknowns ($M$ $N$-dimensional vectors)
$b$ : $K$ $N$-dimensional vectors
$c$ : $K$ known euclideian distances in $R^N$
Can this be expressed as a linear least squares problem? How should I approach this?