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Given a set of matrix $M_i$, by picking a sign coefficient $S_i\in\{-1,1\}$

How can I effectively find a combination that the sum $M^*= \sum_{i=1}^N S_iM_i$ is a nonnegative matrix.

i.e. ${M^*}_{i,j}\geq0$ $\forall i,j$

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    It looks like this problem can be rephrased as an [integer linear programming](http://en.wikipedia.org/wiki/Integer_linear_programming) problem, in which case, software for solving arbitrary integer linear programming instances should be able to handle this task.2012-09-13

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