How might one find integer solutions to:

$$ \textrm{diag}(x)Ax = Bx $$

$A$ and $B$ are integer-valued, square, non-invertible, sparse, and large. The values of $x$ should be $0$ or $1$ (ideally; constraint can be relaxed to include all integers). Are there techniques out there besides MIP?

  • $\begingroup$ By any chance is $B$ nonnegative (or nonpositive)? $\endgroup$
    – prubin
    Commented Jan 25, 2021 at 16:21
  • $\begingroup$ $A$ is non-negative, but $B$ can have both positive and negative values $\endgroup$
    – tphillips
    Commented Jan 25, 2021 at 17:21
  • $\begingroup$ Well, that's unhelpful. $\endgroup$
    – prubin
    Commented Jan 26, 2021 at 18:21


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