[R] Fine tunning rgenoud
Paul Smith
phhs80 at gmail.com
Wed Jul 4 11:59:48 CEST 2007
On 7/4/07, RAVI VARADHAN <rvaradhan at jhmi.edu> wrote:
> 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.
Thanks again, Ravi. Actually, the LP approach also works here. Let
g(X) >= k be the constraints. Then, by solving a LP problem with the
constraints
g(X) >= (k+0.2)
returns an interior starting value for constrOptim. I am aware that
the new set of constraints may correspond to an impossible linear
system, but it works in many cases.
Paul
> ----- 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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