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Daniel Lobo

2025-Mar-27 19:36 UTC

[R] Problem with minimization that I failed to understand

My code is to minimize the objective function

therefore, shouldnt I expect that

StartingValue = 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(q1$par) < Fn(StartingValue)
## FALSE

Below is the corrected code that can be reproduced:

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:dim(MyDat)[1],
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)

Fn(q1$par) < 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))
#FALSE


On Fri, 28 Mar 2025 at 00:58, Rui Barradas <ruipbarradas at sapo.pt>
wrote:
> ?s 18:35 de 27/03/2025, Daniel Lobo escreveu:
> > 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]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> https://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> Hello,
>
> I cannot reproduce your result.
> Instead of checking the result with
>
>
> Fn(c(0.12, 0.04, 0.07, etc, ...)
>
>
> pass the actual return value, q1$par. That's what I did and the result
> matches the function minimum.
> Here is the code I ran.
>
>
>
>
> 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]
> )
>
> Nobs <- nrow(MyDat)
>
> 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
> )
>
> q1$value
> #> [1] -0.1632184
> Fn(q1$par)
> #> [1] -0.1632184
>
>
>
> Hope this helps,
>
> Rui Barradas
>
>
> --
> Este e-mail foi analisado pelo software antiv?rus AVG para verificar a
> presen?a de v?rus.
> www.avg.com
>
	[[alternative HTML version deleted]]

Rui Barradas

2025-Mar-27 22:23 UTC

head link

[R] Problem with minimization that I failed to understand

?s 19:36 de 27/03/2025, Daniel Lobo escreveu:> My code is to minimize the objective function
> 
> therefore, shouldnt I expect that
> 
> StartingValue = 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(q1$par) < Fn(StartingValue)
> ## FALSE
> 
> Below is the corrected code that can be reproduced:
> 
> 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:dim(MyDat)[1],
> 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)
> 
> Fn(q1$par) < 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))
> #FALSE
> 
> 
> On Fri, 28 Mar 2025 at 00:58, Rui Barradas <ruipbarradas at sapo.pt>
wrote:
> 
>> ?s 18:35 de 27/03/2025, Daniel Lobo escreveu:
>>> 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$value
>>> #0.1632184
>>> Fn(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04, 0.09, 0.08,
0.02,
>>> 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02))
>>> #0.1586207
>>>
>>> Could you please help me to understand what went wrong with my code
and
>> how
>>> to correct that?
>>>
>>>        [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>> https://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> Hello,
>>
>> I cannot reproduce your result.
>> Instead of checking the result with
>>
>>
>> Fn(c(0.12, 0.04, 0.07, etc, ...)
>>
>>
>> pass the actual return value, q1$par. That's what I did and the
result
>> matches the function minimum.
>> Here is the code I ran.
>>
>>
>>
>>
>> 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]))
>>     )$tau[1]
>> )
>>
>> Nobs <- nrow(MyDat)
>>
>> q1 <- pracma::fmincon(
>>     c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04, 0.09, 0.08,
>>       0.02, 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02),
>>     fn = Fn,
>>     A = matrix(c(rep(0, 20), -1), nrow = 1), b = -2.05/100,
>>     Aeq = matrix(c(rep(1, 20), 1), nrow = 1), beq = 1,
>>     lb = rep(0.01, 21),
>>     tol = 1e-16,
>>     maxfeval = 10000000,
>>     maxiter = 5000000
>> )
>>
>> q1$value
>> #> [1] -0.1632184
>> Fn(q1$par)
>> #> [1] -0.1632184
>>
>>
>>
>> Hope this helps,
>>
>> Rui Barradas
>>
>>
>> --
>> Este e-mail foi analisado pelo software antiv?rus AVG para verificar a
>> presen?a de v?rus.
>> www.avg.com
>>
> Hello

The code in answer has Kendall::Kendall when it should be
-Kendall::Kendall.

Apparently I removed the minus sign when I reformated the function code.
But without the minus sign I get


q1$value
#> [1] -0.1632184
Fn(q1$par)
#> [1] -0.1632184
Fn(q1$par) < Fn(StartingValue)
#> [1] TRUE


Is there a sign error somewhere?

Hope this helps,

Rui Barradas


-- 
Este e-mail foi analisado pelo software antiv?rus AVG para verificar a presen?a
de v?rus.
www.avg.com

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