I try to understand that, but I have no clue what do to and how to do it.
$A$ is a $m \times n$ matrix with $rg(A)=m$. Find the solution for $Ax = b$, which is regarding to the $2$-norm (I guess that's the Euclidean norm) the shortest.
Problem:
$\min (1/2)x^T*x$
s.t.: $Ax=b$
Hint: Put with the variable $y$ and maximize over $y$ the constraint into the objective function and use the Minimax Lemma.