How can I find the (approximate) solution to the following problem:
$$\text{argmin}_x \|Ax-[Var(Ax)]^{\frac{1}{2}}-b\|^2,$$ where $Var(.)$ denotes the variance? $A$ is matrix and $b$ and $x$ are vectors, and only $x$ is unknown.
EDIT: $$Var(A_ix)=\sqrt{\sum_jP(j|i)(A_jx-\sum_jP(j|i)A_jx)^2}$$
$A_i$ is the $i$-th row of $A$, $P$ is conditional probability mass function.