Consider the quadratic minimization problem of the form :
Finding a vector $x$ that minimizes : $$ \|Ax-b\|_{2}^{2}+\|Bx-c\|_{2}^{2} $$ I am familiar with ordinary least squares problem but this is the first time I encounter such type of least square problems.
I know that by the properties of vector norms, we can bound this expression from below since for any two vectors $u$ and $v$ we know $\|u+v\|_{2}<\|u\|_{2}+\|v\|_{2}$
I would hope for some urgent help.
Notice that $$\|Ax-b\|_{2}^{2}+\|Bx-c\|_{2}^{2} = \left\| \begin{bmatrix}A\\B\end{bmatrix}x - \begin{bmatrix}b\\c\end{bmatrix} \right\|_2^2$$ So this is again a classic least square problem