Interval contractor

In mathematics, an interval contractor (or contractor for short) associated to a set X is an operator C which associates to a box [x] in Rⁿ another box C([x]) of Rⁿ such that the two following properties are always satisfied

A contractor associated to a constraint (such as an equation or an inequality) is a contractor associated to the set X of all x which satisfy the constraint. Contractors make it possible to improve the efficiency of branch-and-bound algorithms classically used in interval analysis.

A contractor C is monotonic if we have ${\displaystyle [x]\subset [y]\Rightarrow C([x])\subset C([y])}$

It is minimal if for all boxes [x], we have ${\displaystyle C([x])=[[x]\cap X]}$, where [A] is the interval hull of the set A, i.e., the smallest box enclosing A.

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