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 <ruipbarra...@sapo.pt> wrote:
> Às 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$value
> > #0.1632184
> > Fn(c(0.12, 0.04, 0.07, 0.03, 0.06, 0.07, 0.07, 0.04, 0.09, 0.08, 0.02,
> > 0.02, 0.03, 0.06, 0.02, 0, 0.07, 0.05, 0.02, 0.02, 0.02))
> > #0.1586207
> >
> > Could you please help me to understand what went wrong with my code and
> how
> > to correct that?
> >
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> https://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> Hello,
>
> I cannot reproduce your result.
> Instead of checking the result with
>
>
> Fn(c(0.12, 0.04, 0.07, etc, ...)
>
>
> pass the actual return value, q1$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
>
>
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