Re: [R] Problem with minimization that I failed to understand

Thu, 27 Mar 2025 15:24:42 -0700 

Às 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 <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?

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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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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


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