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 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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### Famous quotes containing the words relaxation and/or programming:

“Worst of all, there is no sign of any *relaxation* of antisemitism. Logically it has nothing to do with Fascism. But the human race is imitative rather than logical; and as Fascism spreads antisemitism spreads.”

—George Bernard Shaw (1856–1950)

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