Re: st: How to maximize/minimize two equations in Stata

[Mauricio Esteban Cuak <cuak2000@gmail.com>]

Hi Tiago,

I am by no means an expert in optimisation, but you seem to have an
ill-defined problem, since you're trying to optimise with two
objectives in mind.
You could try separately maximising X and minimising Y and checking if
you get the same a.
Otherwise, you need to put some weights on the two objectives.
Say, you could maximize:

t*X - k*Y
Where t and k can be 1 of course.

Best,

M

2011/4/24 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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