In mathematics, the linear programming relaxation of a 0-1 integer program is the problem that arises by replacing the constraint that each variable must be 0 or 1 by a weaker constraint, that each variable belong to the interval .
That is, for each constraint of the form
The resulting relaxation is a linear program, hence the name. This relaxation technique transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.
Read more about Linear Programming Relaxation: Example, Solution Quality of Relaxed and Original Programs, Approximation and Integrality Gap, Branch and Bound For Exact Solutions, Cutting Plane Method
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