st: How to maximize/minimize two equations in Stata

["Tiago V. Pereira" <tiago.pereira@mbe.bio.br>]

Dear Statalisters,

I need to solve a problem in Stata, but I am not sure if Stata is capable
of solving that.

I have checked -nl- and optimize in Mata, but I am not sure if they do
what I am looking for.


The problem I have is the following:

(a*b+(1-a)*c)/((a^2)*d+((1-a)^2)*e+2*a*(1-a)*f) = X

((a^2)*d+((1-a)^2)*e+2*a*(1-a)*f)                     = Y

I need to compute the single parameter "a" in both equations 1 and 2 that
provides the largest value of X, while giving the smallest possible value
of Y. I have all remaining values: b,c,d,e and f.

I am asking you this question because I saw that both -nl- and optimize
set each equation to a specific value. In my case, I don't know the value
of X and Y. I am just interested in the largest possible value of X with
the smallest possible value of Y.


 I will be very grateful if you could provide me some advice/references.

All the best,

Tiago







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