If $a_{m\times 1}$ and $Q_{m\times n}$ ($m<n $) are known, and we know every element of $b$ is between $[1\ \ 1]$, how to determine $b$ to minimize $\a+Qb\_2$?
closed as offtopic by Suvrit, Stefan Kohl, user1688, Wolfgang, Alex Degtyarev Sep 18 '16 at 21:09
This question appears to be offtopic. The users who voted to close gave this specific reason:
 "This question does not appear to be about research level mathematics within the scope defined in the help center." – Stefan Kohl, Community, Wolfgang, Alex Degtyarev

$\begingroup$ Solve it as a quadratic program (using an iterative algorithm). $\endgroup$ – Suvrit Sep 18 '16 at 12:43
There is an algorithm designed specifically for the OP's problem, given in BoundedVariable LeastSquares: an Algorithm and Applications [pdf]:
BVLS (boundedvariable leastsquares) is modelled on NNLS and solves the problem \begin{equation} \min_{l \leq x \leq u} \A x  b\_2, \end{equation} where $l,x,u \in \mathbb{R}^n, b \in \mathbb{R}^m$ and $A$ is an $m$ by $n$ matrix.