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Sep 22, 2014 at 16:10 comment added Andreas Thom I just realize that a positive polynomial does not need to realize its infimum, e.g., $f(x,y)=x^2 + (xy-1)^2$. Hence, the argument above is not complete in this form.
Aug 11, 2014 at 14:28 vote accept yurius
Aug 11, 2014 at 13:01 history answered Andreas Thom CC BY-SA 3.0