Least squares regression with nonnegative error

Question

I'm looking for algorithms to solve a special quadratic programming problem, but I don't know its name or related keywords. Can anyone give me some clues? The problem reads \begin{equation} {\min}_x \left\|Ax-b\right\|^2\\ \mathrm{s.t.}\ Ax-b\geq0 \end{equation} , where $A$ is a $m\times n$ matrix, $x$ is a vector in $\mathbb{R}^n$, and $b$ is a vector in $\mathbb{R}^m$, with $m>n$. This problem can be interpreted as minimizing the squared error but requiring the regression error at each data point to be nonnegative. As the shows, it's a linear regression problem. The blue line shows the ordinary least-squares regression, while the red line is a majorant of these data points obtained by the above QP problem. I notice that there is a similar problem called non-negative least squares, where the inequality constraint is on $x$, not on $Ax-b$.