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A variation of this approach called Hansen's method uses [[Interval arithmetic#History|interval methods]].<ref>{{cite book |last=Leader|first=Jeffery J. | title=Numerical Analysis and Scientific Computation |year=2004|publisher=Addison Wesley |___location= |isbn= 0-201-73499-0 }}</ref> It inherently implements rectangular constraints.
One way for evaluating this upper bound for a partial solution is to consider each soft constraint separately. For each soft constraint, the maximal possible value for any assignment to the unassigned variables is assumed. The sum of these values is an upper bound because the soft constraints cannot assume a higher value. It is exact because the maximal values of soft constraints may derive from different evaluations: a soft constraint may be maximal for <math>x=a</math> while another constraint is maximal for <math>x=b</math>.
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