I have an array ($Y$) with a series of data to which I must fit the sum of some other arrays $(X_1,X_2,X_3)$. The expression is:
$Y = c_1*X_1 + c_2*X_2 + c_3*X_3 + e$
I need to add some constraints (min and max values of $c_1$).
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If you just want to fit a least squares hyperplane with a constraint in one parameter, what I would do is:
$$Y - c_1*X_1 = c_2*X_2 + c_3*X_3 + e$$
That is, now your response is $Y - c_1*X_1$ (an array of known values) and your predictors are $X_2$ and $X_3$.
Please notice that, although this least squares fitting may work, constraints may have effects on procedure and interpretation of significance tests or variable selection.