nloptwrap function

Wrappers for additional optimizers

Wrappers to allow use of alternative optimizers, from the NLopt

library (via list("nloptr")) or elsewhere, for the nonlinear optimization stage.

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

Returns

• 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 list("nloptr") R package), and to the nlminb

optimizer from base R. nlminb is also available via the list("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 list("optimx") (see examples below).

One important difference between the list("nloptr")-provided implementation of BOBYQA and the list("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.
  

Examples

library(lme4)
ls.str(environment(nloptwrap)) # 'defaultControl' algorithm "NLOPT_LN_BOBYQA"
## 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
c(logLik(fm1C) - logLik(fm1)) ## no difference in LL
## 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")
}

Author(s)

Gabor Grothendieck (nlminbwrap)