[R] Non linear optimization with nloptr package fail to produce true optimal result

[Daniel Lobo]

A small correction, the below combination

2.02, 6.764, 6.186, -20.095

Gives better result.

On Fri, 13 Dec 2024 at 23:22, Daniel Lobo <danielobo9976 using gmail.com> 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?