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Non linear System of inequalities


I need a help at solving Non linear System of inequalities in tree
variabels or more for example:
xy<=r<=2xy
xz<=r<=2xz
yz<=r<=2yz
and so on...
my Non linear System of inequalities  represent the constraints at at
some problem which I search (consistency of a model).

  is there any material or sites which may help me?
I will apreciate any help.


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