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In mathematics, an interval contractor (or contractor for short) 〔 〕 associated to a set ''X'' is an operator ''C'' which associates to a box () in R''n'' another box ''C''(()) of R''n'' such that the two following properties are always satisfied * (contractance property) * (completeness property) 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. ==Properties of contractors== A contractor ''C'' is monotonic if we have It is ''minimal'' if for all boxes (), we have , where () is the ''interval hull'' of the set ''A'', i.e., the smallest box enclosing ''A''. The contractor ''C'' is ''thin'' if for all points ''x'', where denotes the degenerated box enclosing ''x'' as a single point. The contractor ''C'' is ''idempotent'' if for all boxes (), we have The contractor ''C'' is ''convergent'' if for all sequences ()(''k'') of boxes containing ''x'', we have 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「interval contractor」の詳細全文を読む スポンサード リンク
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