I reduced a problem of matrix completion to the problem

find $A,B$ such that

$AB=I$

$A_{min}\leq A \leq A_{max}$

$B_{min}\leq B \leq B_{max}$

One possible approach would be to just minimize $\|AB-I\|$ or minimizing $A$ and $B$ alternately. I was wondering whether there is a different, maybe more efficient approach to solve this. I know about the *sign-accord*-algorithm by Jiri Rohn to find strict bounds for the inverse of an interval matrix, but my matrix intervals are not necessarily regular.

In general I know the sign-pattern of the matrices, special cases are that one of the matrices is a (symmetrical) M-matrix. The symmetrical M-matrix case results in particular in a positive definite matrix.