Nelder_Mead: Nelder-Mead Optimization of Parameters, Possibly (Box)...

In lme4/lme4: Linear Mixed-Effects Models using 'Eigen' and S4

Nelder-Mead Optimization of Parameters, Possibly (Box) Constrained

Description

Nelder-Mead optimization of parameters, allowing optimization subject to box constraints (contrary to the default, method = "Nelder-Mead", in R's optim()), and using reverse communications.

Usage

Nelder_Mead(fn, par, lower = rep.int(-Inf, n), upper = rep.int(Inf, n),
            control = list())

Arguments

fn	a function of a single numeric vector argument returning a numeric scalar.
par	numeric vector of starting values for the parameters.
lower	numeric vector of lower bounds (elements may be -Inf).
upper	numeric vector of upper bounds (elements may be Inf).
control	a named list of control settings. Possible settings are iprint numeric scalar - frequency of printing evaluation information. Defaults to 0 indicating no printing. maxfun numeric scalar - maximum number of function evaluations allowed (default:10000). FtolAbs numeric scalar - absolute tolerance on change in function values (default: 1e-5) FtolRel numeric scalar - relative tolerance on change in function values (default:1e-15) XtolRel numeric scalar - relative tolerance on change in parameter values (default: 1e-7) MinfMax numeric scalar - maximum value of the minimum (default: .Machine$double.xmin) xst numeric vector of initial step sizes to establish the simplex - all elements must be non-zero (default: rep(0.02,length(par))) xt numeric vector of tolerances on the parameters (default: xst*5e-4) verbose numeric value: 0=no printing, 1=print every 20 evaluations, 2=print every 10 evalutions, 3=print every evaluation. Sets ‘iprint’, if specified, but does not override it. warnOnly a logical indicating if non-convergence (codes -1,-2,-3) should not stop(.), but rather only call warning and return a result which might inspected. Defaults to FALSE, i.e., stop on non-convergence.

Value

a list with components

fval	numeric scalar - the minimum function value achieved
par	numeric vector - the value of x providing the minimum
convergence	integer valued scalar, if not 0, an error code: -4 nm_evals: maximum evaluations reached -3 nm_forced: ? -2 nm_nofeasible: cannot generate a feasible simplex -1 nm_x0notfeasible: initial x is not feasible (?) 0 successful convergence
message	a string specifying the kind of convergence.
control	the list of control settings after substituting for defaults.
feval	the number of function evaluations.

See Also

The NelderMead class definition and generator function.

Examples

fr <- function(x) {   ## Rosenbrock Banana function
    x1 <- x[1]
    x2 <- x[2]
    100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
p0 <- c(-1.2, 1)

oo  <- optim(p0, fr) ## also uses Nelder-Mead by default
o.  <- Nelder_Mead(fr, p0)
o.1 <- Nelder_Mead(fr, p0, control=list(verbose=1))# -> some iteration output
stopifnot(identical(o.[1:4], o.1[1:4]),
          all.equal(o.$par, oo$par, tolerance=1e-3))# diff: 0.0003865


o.2 <- Nelder_Mead(fr, p0, control=list(verbose=3, XtolRel=1e-15, FtolAbs= 1e-14))
all.equal(o.2[-5],o.1[-5], tolerance=1e-15)# TRUE, unexpectedly

lme4/lme4 documentation built on April 14, 2024, 6:33 a.m.