[Rd] non-differentiable evaluation points in nlminb(), follow-up of PR#15052

From: Sebastian Meyer <Sebastian.Meyer_at_ifspm.uzh.ch>
Date: Wed, 26 Sep 2012 11:13:49 +0200


This is a follow-up question for PR#15052 <http://bugs.r-project.org/bugzilla3/show_bug.cgi?id=15052>

There is another thing I would like to discuss wrt how nlminb() should proceed with NAs. The question is: What would be a successful way to deal with an evaluation point of the objective function where the gradient and the hessian are not well defined?

If the gradient and the hessian both return NA values (assuming R < r60789, e.g. R 2.15.1), and also if both return +Inf values, nlminb steps to an NA parameter vector.
Here is a really artificial one-dimensional example for demonstration:

f <- function (x) {
  cat("evaluating f(", x, ")\n")
  if(is.na(x)) {Inf # to prevent an infinite loop for R < r60789   } else abs(x)
}
gr <- function (x) if (abs(x) < 1e-5) Inf else sign(x) hess <- function (x) matrix(if (abs(x) < 1e-5) Inf else 0, 1L, 1L) trace(gr)
trace(hess)
nlminb(5, f, gr, hess, control=list(eval.max=30, trace=1))

Thus, if nlminb reaches a point where the derivatives are not defined, optimization is effectively lost. Is there a way to deal with such points in nlminb? Otherwise, the objective function is doomed to emergency stop() if it receives NA parameters because nlminb won't pick up courage - regardless of the following return value of the objective function.
As far as I would assess the situation, nlminb is currently not capable of optimizing objective functions with non-differentiable points.

ink2">Best regards,
  Sebastian Meyer

-- 
Sebastian Meyer
Division of Biostatistics
Institute of Social and Preventive Medicine
University of Zurich

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