COBYLA stands for Contrained Optimization by Linear Approximation.
You seem to have some squares in your functions. Maybe BOBYQA would
be a better choice, though it only does bounds, so you'd have to introduce
a penalty, but then more of the optimx solvers would be available. With
only 4 parameters, possibly one of the Nelder-Mead variants (anms?) would
be suitable at least for tryout.
Optimizers are like other tools. Some are chainsaws, others are scalpels.
Don't do neurosurgery with a chainsaw unless you want a mess.
Have you checked that the objective and contraint are computed correctly?
> 50% of "your software doesn't work" in optimization are due to such errors.
John Nash
On 2024-12-13 12:52, Daniel Lobo wrote:
Hi,
I have below non-linear constraint optimization problem
#Original artificial data
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
However this does not appear to be optimal value. For example, if I
use below set,
0.222, 6.999, 6.17, -19.371, value of my objective function is lower
that that using nloptr
I just wonder in the package nloptr is good for non-linear optimization?
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