[R] Nonlinear integer programming (again)

[Zwick, Rebecca J]

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


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