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

[Daniel Lobo]

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.

On Sat, 14 Dec 2024 at 01:14, John Fox <jfox using 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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>