I have a binary integer programming problem for which I only need a solution that meets all the constraints. I do not have an objective function that I am trying to minimize or maximize.
I've been using lp_solve to solve this problem and it works well — I simply define my objective function to be
$$\begin{array}{ll} \text{maximize} & {\bf 0}^T {\bf x}\end{array}$$
However, this seems kind of silly and I keep wondering if there is a better way.
Is there a name for linear programming problems with no objective function? If I don't have an objective function is there some technique more efficient than linear programming (in particular, branch and bound) that I should be using?