[R] Problem with minimization that I failed to understand

[Daniel Lobo]

Hi Duncan,

Thanks for your comment, I agree with that.

But, how it can be justified that an Optimizer gives a result which is
inferior to the starting value? At most, resulting value can remain at the
same level, isnt it?

On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan using gmail.com>
wrote:

> I haven't run your code, but since Kendall correlation is based on
> ranks, your Fn is probably locally constant with jumps when the ranks
> change.  That's a really hard kind of function to maximize, and the
> algorithm used by fmincon is not appropriate to do it.
>
> Sorry, but I don't know if there is an R function that can do
> constrained discrete maximization.
>
> Duncan Murdoch
>
> On 2025-03-27 2:35 p.m., Daniel Lobo wrote:
> > Hi,
> >
> > I have below minimization problem
> >
> >
> > MyDat = structure(list(c(50L, 0L, 0L, 50L, 75L, 100L, 50L, 0L, 50L, 0L,
> > 25L, 50L, 50L, 75L, 75L, 75L, 0L, 75L, 75L, 75L, 0L, 25L, 75L,
> > 75L, 0L, 75L, 100L, 0L, 25L, 100L), c(75L, 0L, 0L, 50L, 100L,
> > 50L, 75L, 75L, 100L, 25L, 0L, 25L, 100L, 0L, 50L, 0L, 25L, 25L,
> > 100L, 75L, 0L, 0L, 0L, 50L, 0L, 75L, 75L, 0L, 50L, 25L), c(50L,
> > 0L, 0L, 0L, 100L, 25L, 0L, 0L, 25L, 50L, 0L, 25L, 75L, 50L, 100L,
> > 50L, 0L, 75L, 25L, 50L, 0L, 0L, 25L, 0L, 50L, 100L, 100L, 0L,
> > 75L, 50L), c(25L, 0L, 0L, 75L, 75L, 25L, 50L, 50L, 100L, 25L,
> > 0L, 100L, 50L, 25L, 100L, 25L, 25L, 100L, 50L, 100L, 0L, 0L,
> > 100L, 50L, 0L, 50L, 75L, 0L, 50L, 25L), c(50L, 0L, 0L, 75L, 75L,
> > 75L, 25L, 25L, 0L, 100L, 0L, 25L, 25L, 75L, 100L, 0L, 25L, 0L,
> > 75L, 25L, 25L, 25L, 75L, 25L, 0L, 75L, 100L, 0L, 100L, 100L),
> >      c(50L, 0L, 0L, 50L, 100L, 25L, 25L, 25L, 50L, 50L, 0L, 50L,
> >      75L, 0L, 100L, 50L, 25L, 100L, 50L, 75L, 0L, 0L, 50L, 25L,
> >      0L, 100L, 100L, 0L, 75L, 50L), c(50L, 0L, 0L, 50L, 75L, 25L,
> >      75L, 50L, 100L, 25L, 0L, 75L, 25L, 0L, 50L, 0L, 50L, 75L,
> >      100L, 75L, 0L, 0L, 100L, 0L, 0L, 50L, 75L, 0L, 100L, 100L
> >      ), c(25L, 75L, 50L, 25L, 75L, 50L, 100L, 75L, 100L, 25L,
> >      0L, 75L, 25L, 50L, 25L, 25L, 75L, 75L, 100L, 75L, 75L, 100L,
> >      75L, 25L, 0L, 75L, 75L, 0L, 75L, 100L), c(55L, 30L, 20L,
> >      30L, 45L, 30L, 30L, 30L, 70L, 30L, 10L, 45L, 45L, 45L, 45L,
> >      30L, 30L, 55L, 45L, 45L, 30L, 30L, 30L, NA, 30L, 55L, 45L,
> >      20L, 45L, 70L), c(85L, 40L, 40L, 40L, 55L, 40L, 20L, 30L,
> >      30L, 30L, 20L, 30L, 70L, 40L, 85L, 55L, 30L, 40L, 30L, 55L,
> >      20L, 30L, 55L, 0L, 40L, 55L, 70L, 40L, 85L, 70L), c(45L,
> >      45L, 0L, 45L, 45L, 45L, 0L, 0L, 100L, 45L, 0L, 100L, 45L,
> >      45L, 100L, 45L, 45L, 100L, 45L, 45L, 45L, 45L, 25L, 45L,
> >      0L, 100L, 45L, 0L, 45L, 45L), c(55L, 45L, 45L, 45L, 55L,
> >      45L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 55L, 55L, 45L,
> >      55L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 55L, 45L, 45L, 45L,
> >      45L), c(100L, 100L, 50L, 100L, 100L, 100L, 100L, 100L, 100L,
> >      100L, 50L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 100L, 50L, 100L, 100L, 100L, 100L, 100L,
> >      100L), c(100L, 25L, 25L, 0L, 100L, 60L, 0L, 0L, 25L, 60L,
> >      0L, 60L, 100L, 60L, 100L, 100L, 25L, 100L, 60L, 100L, 100L,
> >      60L, 100L, 60L, 100L, 100L, 100L, 100L, 60L, 60L), c(0L,
> >      0L, 50L, 50L, 100L, 100L, 0L, 0L, 100L, 100L, 0L, 100L, 100L,
> >      0L, 100L, 100L, 0L, 100L, 100L, 100L, 100L, 100L, 100L, 0L,
> >      100L, 100L, 100L, 100L, 100L, 100L), c(40L, 100L, 40L, 100L,
> >      100L, 40L, 100L, 100L, 100L, 40L, 100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 0L, 100L, 100L), c(100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, -10L,
> >      100L, 100L, 100L, -10L, 100L, 100L), c(70L, 0L, 25L, 0L,
> >      100L, 25L, 0L, 0L, 0L, 45L, 0L, 25L, 100L, 100L, 100L, 100L,
> >      0L, 70L, 0L, 100L, 45L, 45L, 0L, 0L, 100L, 100L, 100L, 0L,
> >      100L, 100L), c(55L, 55L, 55L, 55L, 55L, 55L, 55L, 55L, 55L,
> >      55L, 55L, 55L, 55L, 55L, 55L, 55L, 20L, 55L, 20L, 55L, 20L,
> >      20L, 100L, 55L, 55L, 55L, 55L, 0L, 55L, 55L), c(65L, 65L,
> >      100L, 65L, 100L, 100L, 100L, 100L, 100L, 100L, 100L, 100L,
> >      100L, 100L, 100L, 100L, 65L, 100L, 100L, 100L, 65L, 100L,
> >      0L, 65L, 100L, 100L, 100L, 100L, 100L, 100L), c(85L, 85L,
> >      85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 85L, 56L, 85L,
> >      100L, 85L, 85L, 85L, 0L, 85L, 85L, 85L, 85L, 85L, 85L, 85L,
> >      85L, 28L, 56L, 56L)), row.names = c(NA, -30L), class = "data.frame")
> >
> > Fn = function(Wts) return(-Kendall::Kendall(1:Nobs,
> > rank(-as.vector(as.matrix(MyDat) %*% matrix(Wts, nc = 1)[, 1, drop =
> > T])))$tau[1])
> > q1 = pracma::fmincon(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04,
> > 0.09, 0.08, 0.02, 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02,
> 0.02),
> > fn = Fn,
> >            A = matrix(c(rep(0, 20), -1), nrow = 1), b = -2.05/100, Aeq =
> > matrix(c(rep(1, 20), 1), nrow = 1), beq = 1,
> >            lb = rep(0.01, 21),
> >            tol = 1e-16, maxfeval = 10000000, maxiter = 5000000)
> >
> >
> > However with above code, I got sub-optimal value in terms of minimization
> > of the objective function:
> >
> > q1$value
> > #0.1632184
> > Fn(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04, 0.09, 0.08, 0.02,
> > 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02))
> > #0.1586207
> >
> > Could you please help me to understand what went wrong with my code and
> how
> > to correct that?
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
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> > PLEASE do read the posting guide
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> > and provide commented, minimal, self-contained, reproducible code.
>
>

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