If I have a system:
$y_{n \times 1} = A_{n \times m} x_{m \times 1}$ where $n<m$ and $rank=n$
What kind of optimization/regularization am I doing if I use:
$x=\min\{\|x\|_2^2+1/2\lambda^T(y-Ax)\}$
the part $\|x\|^2_2$ looks like ridge regression with $\lambda=1$ but the remaining part is confusing. It is not the absolute deviation it is only the deviation.
EDIT: After lots of Googling and reading, I discovered that this is called the least-norm solution of the under-determined linear system. Thanks.