On 2024-12-13 5:11 p.m., John Fox wrote:
Dear Daniel,
On 2024-12-13 2:51 p.m., Daniel Lobo wrote:
Caution: External email.
Looks like the solution 1.576708 6.456606 6.195305 -19.007996 is
the best solution that nloptr can produce by increasing the iteration
numbers.
The better set of solution is obtained using pracma package.
Not if I read the output correctly. As I showed, the result from
pracma:fmincon() produces a larger value of the objective function than
the result I obtained from nloptr().
John Nash (who is an expert on optimization -- I'm not) obtained an even
lower value of the objective function from alabama::auglag().
As others have pointed out, one can't really draw general conclusions
from a particular example, and like others, I don't have the time or
inclination to figure out why your problem appears to be ill-conditioned
(though note that the columns of X, excluding the constant, are highly
correlated).
I would guess that the main difficulty with the example is the "sum of
absolute errors" objective function. That objective function has a
discontinuous derivative which will cause problems for many optimizers.
It may also have many local optima, though I don't know in this case.
Duncan Murdoch
Best,
John
On Sat, 14 Dec 2024 at 01:14, John Fox <j...@mcmaster.ca> wrote:
Dear Daniel et al.,
Following on Duncan's remark and examining the message produced by
nloptr(), I simply tried increasing the maximum number of function
evaluations:
------ snip -------
> nloptr(rep(0, 4), f, eval_g_ineq = hin, eval_g_eq = Hx, opts =
+ list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1.0e-8,
+ maxeval = 1e5)
+ )
Call:
nloptr(x0 = rep(0, 4), eval_f = f, eval_g_ineq = hin, eval_g_eq = Hx,
opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-08,
maxeval = 1e+05))
Minimization using NLopt version 2.7.1
NLopt solver status: 4 ( NLOPT_XTOL_REACHED: Optimization stopped
because xtol_rel or xtol_abs (above) was reached. )
Number of Iterations....: 46317
Termination conditions: xtol_rel: 1e-08 maxeval: 1e+05
Number of inequality constraints: 1
Number of equality constraints: 1
Optimal value of objective function: 1287.71725107671
Optimal value of controls: 1.576708 6.456606 6.195305 -19.008
---------- snip ----------
That produces a solution closer to, and better than, the one that you
suggested (which you obtained how?):
> f(c(0.222, 6.999, 6.17, -19.371))
[1] 1325.076
I hope this helps,
John
--
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://www.john-fox.ca/
--
On 2024-12-13 1:45 p.m., Duncan Murdoch wrote:
Caution: External email.
You posted a version of this question on StackOverflow, and were given
advice there that you ignored.
nloptr() clearly indicates that it is quitting without reaching an
optimum, but you are hiding that message. Don't do that.
Duncan Murdoch
On 2024-12-13 12:52 p.m., Daniel Lobo wrote:
library(nloptr)
set.seed(1)
A <- 1.34
B <- 0.5673
C <- 6.356
D <- -1.234
x <- seq(0.5, 20, length.out = 500)
y <- A + B * x + C * x^2 + D * log(x) + runif(500, 0, 3)
#Objective function
X <- cbind(1, x, x^2, log(x))
f <- function(theta) {
sum(abs(X %*% theta - y))
}
#Constraint
eps <- 1e-4
hin <- function(theta) {
abs(sum(X %*% theta) - sum(y)) - 1e-3 + eps
}
Hx <- function(theta) {
X[100, , drop = FALSE] %*% theta - (120 - eps)
}
#Optimization with nloptr
Sol = nloptr(rep(0, 4), f, eval_g_ineq = hin, eval_g_eq = Hx, opts =
list("algorithm" = "NLOPT_LN_COBYLA", "xtol_rel" = 1.0e-8))$solution
# -0.2186159 -0.5032066 6.4458823 -0.4125948
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