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Let $F, g$ be a polynomias in $n$ variables and consider the optimization task $\min F(x) s.t. g(x)=0$ . In Order to solve this with the Lagrange method, one has to find a multipliers. Can one say anything on the dependency of t he multipliers on the coefficients of the polynomials?

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There is only one constraint, thus, only one multiplier. –  Nesbit Jul 2 at 14:18
Well In case g has singular points one needs to be a bit more careful –  Ben Jul 2 at 14:21

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