R help - Feb 2015 - Nonlinear integer programming (again)

Another user suggested I elaborate on my previous post, giving specifics of the
problem I am trying to solve.  Here they are:



It is a selection problem involving sample weights.  Say we have applicants with
test scores x.  The vector y indicates whether the applicant is a member of
Group Y, which is relevant to selection.  The vector w contains the sample
weights.  The vector z is to contain zeroes and ones indicating which applicants
are selected.  I want to maximize the weighted average test score for the
selected applicants, [1/(z'w)]*(z'diag(xw'), under the following
constraints:



All elements of z are either 0 or 1.

Additional constraints are of the form

a ?  z'w ? b  and   z'diag(yw') ? c,

where a, b, and c are positive constants.



The inequality constraints are linear in z, but the quantity to be maximized is
not.

My question is whether there is an R package that can handle this problem.



PREVIOUS POST:

I am seeking an optimization routine that can deal with the following problem:

Maximize g(x), where x is a vector and g is nonlinear, subject to linear
constraints of the form h(x)>0 and m(x)=0 and subject to the constraint that
all values of x are 0 or 1.

I can't find a nonlinear optimization program in R that states that it can
accommodate 0-1 constraints.

Oddly, Excel's Solver will produce a solution to such problems but (1) I
don't trust it and (2) it cannot handle a large number of constraints.


Rebecca Zwick  (Santa Barbara, California)
Statistical Analysis, Data Analysis, and Psychometric Research
Educational Testing Service


________________________________

This e-mail and any files transmitted with it may contain privileged or
confidential information. It is solely for use by the individual for whom it is
intended, even if addressed incorrectly. If you received this e-mail in error,
please notify the sender; do not disclose, copy, distribute, or take any action
in reliance on the contents of this information; and delete it from your system.
Any other use of this e-mail is prohibited.


Thank you for your compliance.

________________________________

	[[alternative HTML version deleted]]

On Sat, 14 Feb 2015, Zwick, Rebecca J wrote:
> My question is whether there is an R package that can handle this problem.
Rebecca,

   I'm not sure, but have you looked at the Simplex method in the boot()
package?

<http://www.astrostatistics.psu.edu/datasets/R/html/boot/html/simplex.html>

Rich

You may have good reason to distrust the Excel solver :)

See below

John Kane
Kingston ON Canada

> -----Original Message-----
> From: rzwick at ets.org
> Sent: Sat, 14 Feb 2015 23:53:55 +0000
> To: r-help at r-project.org
> Subject: [R] Nonlinear integer programming (again)
>
> Oddly, Excel's Solver will produce a solution to such problems but (1)
I
> don't trust it and (2) it cannot handle a large number of constraints.
From IIRC a discussion on the R-help list but which I forgot to save the link.

"The idea that the Excel solver "has a good reputation for being fast
and accurate" does not withstand an examination of the Excel solver's
ability to solve the StRD nls test problems. Solver's ability is abysmal. 13
of 27 "answers" have zero accurate digits, and three more have fewer
than two accurate digits --and this is after tuning the solver to get a good
answer.
...
Excel solver does have the virtue that it will always produce an answer, albeit
one with zero accurate digits."
Bruce McCullough

____________________________________________________________
FREE 3D MARINE AQUARIUM SCREENSAVER - Watch dolphins, sharks & orcas on your
desktop!