# Linear Programming Relaxation

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

of the original integer program, one instead uses a pair of linear constraints

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 RelaxationExample, Solution Quality of Relaxed and Original Programs, Approximation and Integrality Gap, Branch and Bound For Exact Solutions, Cutting Plane Method

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