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I am trying to constrain the coefficients on a higher order polynomial (let's say an order 6) for the curve to be decreasing.

I have found this link, where the fitting of a 3rd order polynomial is being fit, but that will not fit my data unfortunately.

Am I right in assuming that it is technically impossible to constraint a higher order polynomial? This would mean:

f(.)= ax^{6} + bx^{5} + cx^{4} + dx^{3} + ex^{2} + f

Which means:

enter image description here

Which is not possible to solve?

What can I do then to force a constraint on the shape of a higher order polynomial?

Stata_user
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