[R] Problem with minimization that I failed to understand
Duncan Murdoch
murdoch@dunc@n @end|ng |rom gm@||@com
Fri Mar 28 10:04:54 CET 2025
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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