[R] Optimization with nonlinear constraints

[Paul Smith]

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