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

[Ben Bolker]

  It's a long way from "X works better than Y on this particular
problem" to "X is superior to Y".  It's a somewhat loose analogy, but
the 'no free lunch theorem'
<https://en.wikipedia.org/wiki/No_free_lunch_theorem> asserts that if
we consider a broad enough class of optimization problems, *no*
optimization algorithm is uniformly best ...

   That answers question #2 ("no"). Answering question #1 requires a
lot of work digging into the details of the problem, which I don't
have the time & energy to do right now ... someone who knows a lot
more about optimization *might* be able to answer based on previous
experience and background knowledge, but even they might have to spend
a lot of time digging ...


On Fri, Dec 13, 2024 at 3:46 PM Daniel Lobo <danielobo9976 using gmail.com> wrote:
>
> Hi Duncan,
>
> I take your advice.
>
> I posted here in search for a better answer to my problem as I could
> not get that there.
>
> My question is:
> 1. Why nloptr() is failing where other programs can continue with the
> same set of data, numbers, and constraints?
> 2. Is this enough ground to say that nloptr is inferior and user
> should not use this in complex problems?
>
> I wish to get a thoughtful answer to above as my working environment
> only has the nloptr package installed, and it is an isolated system
> due to security issues and installation of a new package requires lot
> lot of approvals and time consuming.
>
> BTW, if someone interested here is my original post
> https://stackoverflow.com/a/79271318/15910619
>
> On Sat, 14 Dec 2024 at 00:15, Duncan Murdoch <murdoch.duncan using gmail.com> wrote:
> >
> > 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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