If an optimal solution to the LP relaxation of an IP is not integer, can we always get a feasible IP solution by rounding it to the nearest integer? Or can we generalize this process by saying, if we have a minimization problem, round it up; if it is a maximization problem, round it down and it will be feasible for the IP. Thanks.
2026-03-29 15:54:33.1774799673
Solution of the LP relaxation - always round to the nearest integer?
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It is fairly trivial to construct a linear program with no feasible integer solution, so the answer to your question as stated would be no.