Wrappers for additional optimizers

Wrappers to allow use of alternative optimizers, from the NLopt library (via nloptr) or elsewhere, for the nonlinear optimization stage.

Usage

nloptwrap (par, fn, lower, upper, control = list(), ...)
nlminbwrap(par, fn, lower, upper, control = list(), ...)

Arguments

par: starting parameter vector
fn: objective function
lower, upper: numeric vector of lower and upper bounds.
control: list of control parameters, corresponding to optCtrl = *, e.g., in lmerControl(). For nloptwrap, see defaultControl in ‘Details’.
...: additional arguments to be passed to objective function

Value

par: estimated parameters
fval: objective function value at minimum
feval: number of function evaluations
conv: convergence code (0 if no error)
message: convergence message

Details

Using alternative optimizers is an important trouble-shooting tool for mixed models. These wrappers provide convenient access to the optimizers provided by Steven Johnson's NLopt library (via the nloptr R package), and to the nlminb optimizer from base R. nlminb is also available via the optimx package; this wrapper provides access to nlminb() without the need to install/link the package, and without the additional post-fitting checks that are implemented by optimx (see examples below).

One important difference between the nloptr-provided implementation of BOBYQA and the minqa-provided version accessible via optimizer="bobyqa" is that it provides simpler access to optimization tolerances. bobyqa provides only the rhoend parameter (“[t]he smallest value of the trust region radius that is allowed”), while nloptr provides a more standard set of tolerances for relative or absolute change in the objective function or the parameter values (ftol_rel, ftol_abs, xtol_rel, xtol_abs).

The default (empty) control list corresponds to the following settings:

nlminbwrap:

control exactly corresponds to nlminb()'s defaults, see there.

nloptwrap:

environment(nloptwrap)$defaultControl contains the defaults, notably algorithm = "NLOPT_LN_BOBYQA".

nloptr::nloptr.print.options() shows and explains the many possible algorithm and options.

Author

Gabor Grothendieck (nlminbwrap)

Examples

library(lme4)
ls.str(environment(nloptwrap)) # 'defaultControl' algorithm "NLOPT_LN_BOBYQA"
#> defaultControl : List of 4
#>  $ algorithm: chr "NLOPT_LN_BOBYQA"
#>  $ xtol_abs : num 1e-08
#>  $ ftol_abs : num 1e-08
#>  $ maxeval  : num 1e+05
## Note that  'optimizer =  "nloptwrap"' is now the default for lmer() :
fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
## tighten tolerances
fm1B <- update(fm1, control= lmerControl(optCtrl = list(xtol_abs=1e-8, ftol_abs=1e-8)))
## run for longer (no effect in this case)
fm1C <- update(fm1,control = lmerControl(optCtrl = list(maxeval=10000)))

  logLik(fm1B) - logLik(fm1)  ## small difference in log likelihood
#> 'log Lik.' 0 (df=6)
c(logLik(fm1C) - logLik(fm1)) ## no difference in LL
#> [1] 0
## Nelder-Mead
fm1_nloptr_NM <- update(fm1, control=
                  lmerControl(optimizer = "nloptwrap",
                              optCtrl = list(algorithm = "NLOPT_LN_NELDERMEAD")))
## other nlOpt algorithm options include NLOPT_LN_COBYLA, NLOPT_LN_SBPLX, see
if(interactive())
  nloptr::nloptr.print.options()

fm1_nlminb <- update(fm1, control=lmerControl(optimizer = "nlminbwrap"))
if (require(optimx)) { ## the 'optimx'-based nlminb :
  fm1_nlminb2 <- update(fm1, control=
                lmerControl(optimizer = "optimx",
                            optCtrl = list(method="nlminb", kkt=FALSE)))
  cat("Likelihood difference (typically zero):  ",
      c(logLik(fm1_nlminb) - logLik(fm1_nlminb2)), "\n")
}
#> Likelihood difference (typically zero):   0