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Daniel Lobo

2025-Mar-28 13:59 UTC

[R] Problem with minimization that I failed to understand

Hi Duncan,

Thanks for your comment, I agree with that.

But, how it can be justified that an Optimizer gives a result which is
inferior to the starting value? At most, resulting value can remain at the
same level, isnt it?

On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan at gmail.com>
wrote:
> 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]]
> >
> > ______________________________________________
> > 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.
>
>
	[[alternative HTML version deleted]]

J C Nash

2025-Mar-28 15:44 UTC

head link

[R] Problem with minimization that I failed to understand

Every time I give a seminar on optimization (most recently in Feb
at Univ Cote d'Azur -- thank you Yassine for the welcome!) I point out

    Algorithms CONVERGE
    Programs  TERMINATE

If you race a Maserati (fmincon?) on a dirt bike course, you'll likely
get stuck on the first mud mound, which could be higher than the start.
You might to better with a Nelder-Mead type minimizer, setting the
objective very large when constraints violated, but ensuring starting
polytope is all-feasible. Not guaranteed, but NM methods are surprisingly
robust. My experience is that they get "near" a local min quite
quickly,
then take forever to decide they're done. And if you have quite large
flat areas, polytope may collapse. I'm suggesting this as I don't have
knowledge of a discrete optimizer in R.

JN




On 2025-03-28 09:59, Daniel Lobo wrote:> Hi Duncan,
> 
> Thanks for your comment, I agree with that.
> 
> But, how it can be justified that an Optimizer gives a result which is
> inferior to the starting value? At most, resulting value can remain at the
> same level, isnt it?
> 
> On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan at
gmail.com>
> wrote:
> 
>> 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]]
>>>
>>> ______________________________________________
>>> 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.
>>
>>
> 
> 	[[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.

Duncan Murdoch

2025-Mar-28 16:08 UTC

head link

[R] Problem with minimization that I failed to understand

That's a question for the maintainer of the package you used.

Duncan Murdoch

On 2025-03-28 9:59 a.m., Daniel Lobo wrote:> Hi Duncan,
> 
> Thanks for?your comment, I agree with that.
> 
> But, how it can be justified that an Optimizer gives a result which is 
> inferior to the starting value? At most, resulting value can remain at 
> the same level, isnt it?
> 
> On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan at
gmail.com
> <mailto:murdoch.duncan at gmail.com>> wrote:
> 
>     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]]
>      >
>      > ______________________________________________
>      > R-help at r-project.org <mailto:R-help at r-project.org>
mailing list
>     -- To UNSUBSCRIBE and more, see
>      > https://stat.ethz.ch/mailman/listinfo/r-help
>     <https://stat.ethz.ch/mailman/listinfo/r-help>
>      > PLEASE do read the posting guide
>     https://www.R-project.org/posting-guide.html
>     <https://www.R-project.org/posting-guide.html>
>      > and provide commented, minimal, self-contained, reproducible
code.
>

Rui Barradas

2025-Mar-28 20:18 UTC

head link

[R] Problem with minimization that I failed to understand

?s 13:59 de 28/03/2025, Daniel Lobo escreveu:> Hi Duncan,
> 
> Thanks for your comment, I agree with that.
> 
> But, how it can be justified that an Optimizer gives a result which is
> inferior to the starting value? At most, resulting value can remain at the
> same level, isnt it?
> 
> On Fri, 28 Mar 2025 at 14:34, Duncan Murdoch <murdoch.duncan at
gmail.com>
> wrote:
> 
>> 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]]
>>>
>>> ______________________________________________
>>> 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.
>>
>>
> 
> 	[[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 don't know if this is relevant a package GA - genetic algorithms - 
gets solutions above the starting value.



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)
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)

library(GA)
#> Loading required package: foreach
#> Loading required package: iterators
#> Package 'GA' version 3.2.4
#> Type 'citation("GA")' for citing this R package in
publications.
#>
#> Attaching package: 'GA'
#> The following object is masked from 'package:utils':
#>
#>     de

set.seed(2025)
g1 <- ga(
   type = "real-valued",
   fitness = \(x) Fn(x),
   lower = rep(0.01, 21),
   upper = rep(1, 21L),
   maxiter = 100L
)
dim(g1 at solution)
#> [1] 21 21
apply(g1 at solution, 1L, Fn)
#>  [1] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 
0.2735632
#>  [8] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 
0.2735632
#> [15] 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 0.2735632 
0.2735632
Fn(StartingValue)
#> [1] 0.1586207

suggestions <- g1 at solution
g2 <- ga(
   type = "real-valued",
   fitness = function(x) Fn(x),
   lower = rep(0.01, 21),
   upper = rep(1, 21L),
   suggestions = suggestions,
   maxiter = 100L
)

dim(g2 at solution)
#> [1] 41 21
apply(g2 at solution, 1L, Fn)
#>  [1] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 
0.2873563
#>  [8] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 
0.2873563
#> [15] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 
0.2873563
#> [22] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 
0.2873563
#> [29] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 
0.2873563
#> [36] 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563 0.2873563
Fn(StartingValue)
#> [1] 0.1586207


Hoep this helps,

Rui Barradas


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