Average linear least squares regression (Q1074336)

We describe an algorithm and a corresponding FORTRAN subroutine for finding a regression vector x with n components such that \[ F(x)=\sum^{s}_{i=1}w_ i\| A_ ix-b_ i\| \] is minimized, where \(\| \cdot \|\) denotes the Euclidean norm, \(w_ i>0,A_ i\) are design matrices with \(m_ i\) rows and n columns, and \(b_ i\) are observation vectors with \(m_ i\) components \((i=1,...s)\).