[R] Optim with two constraints

[Berwin A Turlach]

>>>>> "AD" == Alexis Diamond <alexisjdiamond at gmail.com> writes:

    AD> I have a follow-up from Jens's question and Professor Ripley's
    AD> response.

    AD> Jens wants to do quadratic optimization with 2 constraints:

    >> > > # I need two constraints:
    >> > > # 1. each element in par needs to be between 0 and 1
    >> > > # 2. sum(par)=1, i.e. the elements in par need to sum to 1

    AD> how does one set both constraints in quadprog, per
    AD> Prof. Ripley's suggestion?  i know how to get quadprog to
    AD> handle the second constraint,
The first is actually not one constraint but 2*k constraints, where k
is the number of elements in "par".  But there is quite some
redundancy in this set of equation.  It suffices to constrain each
element to be bigger or equal to 0 and that they should sum to 1.  If
these constraints are fulfilled, then each element must be less or
equal to one.

    AD> but not BOTH, since quadprog only takes as inputs the
    AD> constraint matrix "A" and constraint vector "b"--
So what stops you from coding the k constraints from 1.) in the form
that quadprog requires them?  From memory, i.e. untested:

m <- length(par)
Amat <- cbind(rep(1,m), diag(m))
bvec <- c(1,rep(0,m))
meq <- 1

solve.QP(Dmat, dvec, Amat, bvec, meq)

    AD> unlike in "ipop" (kernlab), there is no additional option for
    AD> box constraints.
Well, the problems that I had (and still have) usually don't involve
box constraints, but I see that other people use them again and again.
So probably it would be a good idea to implement them...  But, more
importantly, would be to implement Powell's modifications of the
Goldfarb-Idnani algorithm to make it numerically more robust...  Oh,
yeah, and a warm start option from a feasible point would be nice
too....  Probably all in a future version which should be released
sometime before Xmas 20xx. :)

    AD> apologies if i am not seeing something obvious here.
Apologies accepted. :)

Cheers,

        Berwin