Following is a doubt I got when I was reading Csiszar's Annals of Statistics paper "Why least squares and maximum entropy: An axiomatic approach to inference for linear inverse problems". He comes up with a set of axioms to justify $\ell_2$-norm minimisation in $\mathbb{R}^n$.

He also argues that $\ell_2$-norm minimization would not be appropriate if the space we consider consists of vectors with positive components,say, $\mathbb{R}_+^n$. Further he says that there exists sets of the form

$$L=\{v \in \mathbb{R}_+^n :Av=b\}$$

where $A$ is some $k\times n$ matrix and $u\notin L$ such that $\min_{v\in L}\|v-u\|_2$ is not attained in $L$.

I can't think of such an example.

Can someone think of such an example?