[R] non-linear contrained optimization

[Prof. John C Nash]

If the data is fairly small, send it and the objective function to me off-list and I'll 
give it a quick try.

However, this looks very much like the kind of distance-constrained type of problem like 
the "largest small polygon" i.e., what is the maximum area hexagon where no vertex is more 
than 1 unit from another. (It is NOT a regular hexagon! More like a dented pentagon.)
Such problems are often better posed using polar coordinates, but the setup takes work.

If you are going to have to do a lot of these problems, it will be worthwhile looking into 
ways to get very good starts, in which case a very crude method using penalty or barrier 
functions could be effective.

John Nash



> From: Brandon Zicha <brandon.zicha at ua.ac.be>
> Subject: [R] non-linear contrained optimization
> Message-ID: <33C13A02-F603-410A-871D-E78DDE272768 at ua.ac.be>
> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
> 
> I have searched the previous help boards and discovered the problem  
> with Rdonlp2 - Specifically, its non-availability. I thought that this  
> was my solution, but perhaps there is a better way that you all could  
> help me with.  I imagine that this problem is trivial to people such  
> as the experts on this mailing list.
> 
> I am trying to solve this problem over and over again in a simulation:
> 
> I want to find the values of x and y which minimize
> f(x,y) = sqrt((z-x)2+(w-y)2
> 
> subject to the constraints:
> 0=< sqrt((z2-x)2+(w2-y)2) - d2
> 0=< sqrt((z3-x)2+(w3-y)2) - d3
> .....
> 0=< sqrt((zk-x)2+(wk-y)2) - dk
> 
> where zi, wi, di are known scalars.
> 
> I would appreciate any help with how to implement this in R.
> 
> Many thanks,
> 
> Brandon Z.
> 
> University of Antwerp