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

Fri, 28 Mar 2025 02:05:23 -0700

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 https://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.






















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