[R] Fine tunning rgenoud

[RAVI VARADHAN]

Paul,

Here is another approach: I wrote an R function that would generate interior points as starting values for constrOptim.  This might work better than the LP approach, since the LP approach gives you a starting value that is on the boundary of the feasible region, i.e a vertex of the polyhedron, whereas this new approach gives you points on the interior.  You can generate as many points as you wish, but the approach is brute-force and is very inefficient - it takes on the order of a 1000 tries to find one feasible point.

Hope this helps,
Ravi. 

----- Original Message -----
From: Paul Smith <phhs80 at gmail.com>
Date: Tuesday, July 3, 2007 7:32 pm
Subject: Re: [R] Fine tunning rgenoud
To: R-help <r-help at stat.math.ethz.ch>


> On 7/4/07, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
>  > It should be easy enough to check that your solution is valid (i.e. 
> a local
>  > minimum):  first, check to see if the solution satisfies all the
>  > constraints; secondly, check to see if it is an interior point 
> (i.e. none of
>  > the constraints become equality); and finally, if the solution is an
>  > interior point, check to see whether the gradient there is close to 
> zero.
>  > Note that if the solution is one of the vertices of the polyhedron, 
> then the
>  > gradient may not be zero.
>  
>  I am having bad luck: all constraints are satisfied, but the solution
>  given by constrOptim is not interior; the gradient is not equal to
>  zero.
>  
>  Paul
>  
>  
>  > -----Original Message-----
>  > From: r-help-bounces at stat.math.ethz.ch
>  > [ On Behalf Of Paul Smith
>  > Sent: Tuesday, July 03, 2007 5:10 PM
>  > To: R-help
>  > Subject: Re: [R] Fine tunning rgenoud
>  >
>  > On 7/3/07, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
>  > > You had indicated in your previous email that you are having trouble
>  > finding
>  > > a feasible starting value for constrOptim().  So, you basically 
> need to
>  > > solve a system of linear inequalities to obtain a starting point. 
>  Have
>  > you
>  > > considered using linear programming? Either simplex() in the "boot"
>  > package
>  > > or solveLP() in "linprog" would work.  It seems to me that you 
> could use
>  > any
>  > > linear objective function in solveLP to obtain a feasible 
> starting point.
>  > > This is not the most efficient solution, but it might be worth a 
> try.
>  > >
>  > > I am aware of other methods for generating n-tuples that satisfy 
> linear
>  > > inequality constraints, but AFAIK those are not available in R.
>  >
>  > Thanks, Ravi. I had already conceived the solution that you suggest,
>  > actually using "lpSolve". I am able to get a solution for my problem
>  > with constrOptim, but I am not enough confident that the solution is
>  > right. That is why I am trying to get a solution with rgenoud, but
>  > unsuccessfully until now.
>  >
>  > Paul
>  >
>  >
>  >
>  > > -----Original Message-----
>  > > From: r-help-bounces at stat.math.ethz.ch
>  > > [ On Behalf Of Paul Smith
>  > > Sent: Tuesday, July 03, 2007 4:10 PM
>  > > To: R-help
>  > > Subject: [R] Fine tunning rgenoud
>  > >
>  > > Dear All,
>  > >
>  > > I am trying to solve the following maximization problem, but I cannot
>  > > have rgenoud giving me a reliable solution.
>  > >
>  > > Any ideas?
>  > >
>  > > Thanks in advance,
>  > >
>  > > Paul
>  > >
>  > > ----------------------------
>  > > library(rgenoud)
>  > >
>  > > v <- 0.90
>  > > O1 <- 10
>  > > O2 <- 20
>  > > O0 <- v*O1+(1-v)*O2
>  > >
>  > > myfunc <- function(x) {
>  > >   U0 <- x[1]
>  > >   U1 <- x[2]
>  > >   U2 <- x[3]
>  > >   q0 <- x[4]
>  > >   q1 <- x[5]
>  > >   q2 <- x[6]
>  > >   p <- x[7]
>  > >
>  > >   if (U0 < 0)
>  > >     return(-1e+200)
>  > >   else if (U1 < 0)
>  > >     return(-1e+200)
>  > >   else if (U2 < 0)
>  > >     return(-1e+200)
>  > >   else if ((U0-(U1+(O1-O0)*q1)) < 0)
>  > >     return(-1e+200)
>  > >   else if ((U0-(U2+(O2-O0)*q2)) < 0)
>  > >     return(-1e+200)
>  > >   else if ((U1-(U0+(O0-O1)*q0)) < 0)
>  > >     return(-1e+200)
>  > >   else if ((U1-(U2+(O2-O1)*q2)) < 0)
>  > >     return(-1e+200)
>  > >   else if((U2-(U0+(O0-O2)*q0)) < 0)
>  > >     return(-1e+200)
>  > >   else if((U2-(U1+(O1-O2)*q1)) < 0)
>  > >     return(-1e+200)
>  > >   else if(p < 0)
>  > >     return(-1e+200)
>  > >   else if(p > 1)
>  > >     return(-1e+200)
>  > >   else if(q0 < 0)
>  > >     return(-1e+200)
>  > >   else if(q1 < 0)
>  > >     return(-1e+200)
>  > >   else if(q2 < 0)
>  > >     return(-1e+200)
>  > >   else
>  > >
>  > return(p*(sqrt(q0)-(O0*q0+U0))+(1-p)*(v*(sqrt(q1)-(O1*q1+U1))+(1-v)*(sqrt(q2
>  > > )-(O2*q2+U2))))
>  > >
>  > > }
>  > >
>  > genoud(myfunc,nvars=7,max=T,pop.size=6000,starting.values=runif(7),wait.gene
>  > > rations=150,max.generations=300,boundary.enforcement=2)
>  > >
>  > > ______________________________________________
>  > > R-help at stat.math.ethz.ch mailing list
>  > > 
>  > > PLEASE do read the posting guide
>  > 
>  > > and provide commented, minimal, self-contained, reproducible code.
>  > >
>  >
>  > ______________________________________________
>  > R-help at stat.math.ethz.ch mailing list
>  > 
>  > PLEASE do read the posting guide 
>  > and provide commented, minimal, self-contained, reproducible code.
>  >
>  
>  ______________________________________________
>  R-help at stat.math.ethz.ch mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code. 
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