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

[Daniel Lobo]

Adding R help

On Fri, 13 Dec 2024 at 23:39, Daniel Lobo <danielobo9976 using gmail.com> wrote:
>
> If I use "algorithm" = "BOBYQA", the nloptr() fails with below message
>
> Error in is.nloptr(ret) :
>
>   Incorrect algorithm supplied. Use one of the following:
>
> NLOPT_GN_DIRECT
>
> NLOPT_GN_DIRECT_L
>
> NLOPT_GN_DIRECT_L_RAND
>
> NLOPT_GN_DIRECT_NOSCAL
>
> NLOPT_GN_DIRECT_L_NOSCAL
>
> NLOPT_GN_DIRECT_L_RAND_NOSCAL
>
> NLOPT_GN_ORIG_DIRECT
>
> NLOPT_GN_ORIG_DIRECT_L
>
> NLOPT_GD_STOGO
>
> NLOPT_GD_STOGO_RAND
>
> NLOPT_LD_SLSQP
>
> NLOPT_LD_LBFGS_NOCEDAL
>
> NLOPT_LD_LBFGS
>
> NLOPT_LN_PRAXIS
>
> NLOPT_LD_VAR1
>
> NLOPT_LD_VAR2
>
> NLOPT_LD_TNEWTON
>
> NLOPT_LD_TNEWTON_RESTART
>
> NLOPT_LD_TNEWTON_PRECOND
>
> NLOPT_LD_TNEWTON_PRECOND_RESTART
>
> NLOPT_GN_CRS2_LM
>
> NLOPT_GN_MLSL
>
> NLOPT_GD_MLSL
>
> NLOPT_GN_MLSL_LDS
>
> NLOPT_GD_MLSL_LDS
>
> NLOPT_LD_MMA
>
> NLOPT_LD_CCSAQ
>
> NLOPT_LN_COBYLA
>
> NLOPT_LN_NEWUOA
>
> NLOPT_LN_NEWUOA_BOUND
>
> NLOPT_LN_NELDERMEAD
>
> NLOPT_LN_SBPLX
>
> NLOPT_LN_AUGLAG
>
> NLOPT_LD_AUGLAG
>
> NLOPT_LN_AUGLAG_EQ
>
> NLOPT_LD_AUGLAG_EQ
>
> NLOPT_LN_BOBYQA
>
> NLOPT_GN_ISRES
>
> NLOPT_GN_ESCH
>
>
> On Fri, 13 Dec 2024 at 23:33, J C Nash <profjcnash using gmail.com> wrote:
> >
> > 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?
> > >
> > > ______________________________________________
> > > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible code.
> >

-------------- next part --------------
A non-text attachment was scrubbed...
Name: dummy.png
Type: image/png
Size: 163 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20241213/f6a8a348/attachment.png>