[R] L-BFGS-B needs finite values of 'fn'

Ravi Varadhan rvaradhan at jhmi.edu
Thu Apr 3 17:38:10 CEST 2008

```Paul,

After looking at your objective function and the penalty, I realized that
since the contribution of each term to the objective function decreases
geometrically, the later terms contribute relatively less to the overall
maximum.  Hence the numerical estimation of those terms is much less precise
compared to the dominant terms.  This explains why the ratios of x[k]/x[k-1]
is not close to b, for small values of b.

Now let us try a larger value of b, say, b=0.8.

Here are the results from optim, with "BFGS".

>  k <- 10000
>  b <- 0.8
>
>  f <- function(x, pen, k, b) {
+  n <- length(x)
+  r <- sum((b^(0:(n-1)))*log(x)) - pen*(sum(x)-k)^2
+  return(r)
+  }
>
>  gr <- function(x, pen, k, b) {
+  n <- length(x)
+  r <- (b^(0:(n-1)))*(1/x) - 2*pen*(sum(x)-k)
+  return(r)
+  }
>
>
> nvar <- 10
> p0 <- runif(nvar, 0, 20)
> sols <- optim(p0, f, gr, method="BFGS", control=list(fnscale=-1), k=k,
b=b, pen=1)
> sum(sols\$par)
[1] 10000
> sols\$par[2:nvar] / sols\$par[1:(nvar-1)]
[1] 0.8038902 0.8021216 0.7974323 0.7999681 0.7983918 0.8006497 0.8013940
[8] 0.8044702 0.7879365
>
>

As you can see, things are much better!

Hope this helps,
Ravi.
----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

----------------------------------------------------------------------------
--------

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Ravi Varadhan
Sent: Wednesday, April 02, 2008 2:03 PM
To: 'Paul Smith'; 'R-help'
Subject: Re: [R] L-BFGS-B needs finite values of 'fn'

Yes, that is very important.  If you look at the ratios x[k]/x[k-1], they
are very close to 0.3 for the first few components, and then they start
slowly diverging (ratio becomes smaller than 0.3) from that.

So, optim is indeed finding a correct solution to the problem that you
"actually" posed.  You could increase your penalty to get a solution that is
closer to the analytical solution you are expecting.

Ravi.

----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

----------------------------------------------------------------------------
--------

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Paul Smith
Sent: Wednesday, April 02, 2008 1:57 PM
To: R-help
Subject: Re: [R] L-BFGS-B needs finite values of 'fn'

But let me add the following: the part

- 2000000*(sum(x)-k)^2

of my function is a penalty. In truth, I want to maximize

sum((b^(0:(n-1)))*log(x))

s.t.

sum(x) = k.

Paul

On Wed, Apr 2, 2008 at 6:48 PM, Paul Smith <phhs80 at gmail.com> wrote:
> Thanks, Ravi. The analytical solution, (x_1,x_2,...,x_10), should
>  satisfy this equality:
>
>  x_t / x_(t-1) = 0.3.
>
>  Unfortunately, the procedure that you suggest does not lead to a
>  solution that satisfies such an equality.
>
>  Paul
>
>
>
>
>
>  On Wed, Apr 2, 2008 at 5:12 PM, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
>  > Paul,
>  >
>  >  Have you tried using "BFGS" without bounds?
>  >
>  >  sols <- optim(rep(20,nvar), f, gr, method="BFGS",
control=list(fnscale=-1))
>  >
>  >  This converges to a solution, although I don't know if the converged
>  >  solution is what you want.
>  >
>  >  Ravi.
>  >
>  >
----------------------------------------------------------------------------
>  >  -------
>  >
>  >  Ravi Varadhan, Ph.D.
>  >
>  >  Assistant Professor, The Center on Aging and Health
>  >
>  >  Division of Geriatric Medicine and Gerontology
>  >
>  >  Johns Hopkins University
>  >
>  >  Ph: (410) 502-2619
>  >
>  >  Fax: (410) 614-9625
>  >
>  >  Email: rvaradhan at jhmi.edu
>  >
>  >  Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>  >
>  >
>  >
>  >
----------------------------------------------------------------------------
>  >  --------
>  >
>  >
>  >
>  >  -----Original Message-----
>  >  From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On
>  >  Behalf Of Paul Smith
>  >
>  > Sent: Monday, March 31, 2008 2:25 PM
>  >  To: R-help
>  >
>  >
>  > Subject: Re: [R] L-BFGS-B needs finite values of 'fn'
>  >
>  >  On Mon, Mar 31, 2008 at 2:57 PM, Zaihra T <zaihra at uwindsor.ca> wrote:
>  >  > try something like  this before wrapping up your function else i
guess
>  >  u'll
>  >  > have to stick to Prof Brian Ripley  suggestion his suggestions are
usually
>  >  > best bet .
>  >  >
>  >  >  f <- function(x) {
>  >  >
>  >  >  n <- length(x)
>  >  >
>  >  > r <- sum((b^(0:(n-1)))*log(x)) - 2000000*(sum(x)-k)^2
>  >  >  if(!is.finite(r))
>  >  >
>  >  > r<-1e+20 return(r)
>  >  >
>  >  > }
>  >  >
>  >  > have a nice day.
>  >  >
>  >  >
>  >  >
>  >  >
>  >  > On Mon, 31 Mar 2008 12:24:09 +0100 "Paul Smith" wrote:
>  >  > > Dear All,
>  >  > >
>  >  > > I am trying to solve the optimization problem below, but I am
always
>  >  > > getting the following error:
>  >  > >
>  >  > > Error in optim(rep(20, nvar), f, gr, method = "L-BFGS-B", lower =
rep(0,
>  >  :
>  >  > > L-BFGS-B needs finite values of 'fn'
>  >  > >
>  >  > > Any ideas?
>  >  > >
>  >  > > Thanks in advance,
>  >  > >
>  >  > > Paul
>  >  > >
>  >  > > -----------------------------------------! ------
>  >  > >
>  >  > > k <- 10000
>  >  > > b <- 0.3
>  >  > >
>  >  > > f <- function(x) {
>  >  > >
>  >  > > n <- length(x)
>  >  > >
>  >  > > r <- sum((b^(0:(n-1)))*log(x)) - 2000000*(sum(x)-k)^2
>  >  > >
>  >  > > return(r)
>  >  > >
>  >  > > }
>  >  > >
>  >  > > gr <- function(x) {
>  >  > >
>  >  > > n <- length(x)
>  >  > >
>  >  > > r <- (b^(0:(n-1)))*(1/x) - 4000000*(sum(x)-k)
>  >  > >
>  >  > > return(r)
>  >  > >
>  >  > > }
>  >  > >
>  >  > > nvar <- 10
>  >  > > (sols <-
>  >  > >
>  >  >
>  >
optim(rep(20,nvar),f,gr,method="L-BFGS-B",lower=rep(0,nvar),upper=rep(k,nvar
>  >
),control=list(fnscale=-1,parscale=rep(2000,nvar),factr=1e-300,pgtol=1e-300)
>  >  ))
>  >
>  >  Not much progress, Zaihra. Unfortunately! I am wondering whether one
>  >  can transform the original problem into an equivalent one and solvable
>  >  with optim.
>  >
>  >  I know the analytical solution; I am just trying to check how far can
>  >  R go regarding optimization problems.
>  >
>  >  Paul
>  >
>  >  ______________________________________________
>  >
>  > R-help at r-project.org mailing list
>  >  https://stat.ethz.ch/mailman/listinfo/r-help
>  >  PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>  >
>  >
>  > and provide commented, minimal, self-contained, reproducible code.
>  >
>

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

```

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