Re: [R] Optimization with nonlinear constraints

From: Paul Smith <phhs80_at_gmail.com>
Date: Wed, 26 Mar 2008 16:21:12 +0000

On Wed, Mar 26, 2008 at 1:17 PM, Andreas Klein <klein82517_at_yahoo.de> wrote:
> I have some further problems with modelling an
> optimization problem in R:
>
> How can I model some optimization problem in R with a
> linear objective function with subject to some
> nonlinear constraints?
> I would like to use "optim" or "constrOptim", maybe
> with respect to methods like "Simulated Annealing" or
> "Sequential Quadric Programming" or something else,
> which can solve the problem. But I have no idea how to
> code in R!
>
> Example:
> min (x1 + x2 + x3)
> s.t.
> p * (a*x1 + b*x2 + c*x3)^(-3) + (1-p) * (d*x1 + e*x2 +
> f*x3)^(-3) >= g
>
> with a,b,c,d,e,f,g,p constant > 0 and x1,x2,x3 > 0
> also: a,b,c > d,e,f
>
>
> I hope you can help me with some code for the above
> problem so I can transfer it to my "real" problem. You
> can also put some real numbers for the above problem.
> I only wanted to abstract the problem with some
> general constant.

I think that your optimization problem, Andreas, has no solution, but please correct me if I am wrong. In fact, when x1, x2 and x3 tend simultaneously to zero, the constrain is satisfied; the minimum would then be x1 = x2 = x3 = 0, but by your assumption, x1,x2,x3 > 0. Thus, the search for the minimum would be endless; no minimum exists.

Paul



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