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Usually this is a relation of the form of an inequality, g(x) <= 0, or equation, h(x)=0. More generally, it can be any restriction the decision variables must satisfy. For example, some regard "x must be integer-valued" as a constraint, while others would say that this is simply the domain of the decision variables in the mathematical program. There are other relations, such as the logical form of a precedence constraint: IF x=0 THEN y=0.

In constraint programming, a constraint is an arbitrary relation imposed on a set of variables LaTeX: X = \{x_1, \dots, x_n\} where each variable must be assigned on value from its domain. A constraint holds if all variables in LaTeX: X are assigned values from their domain and the relation is satisfied.

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