# nlminb

0th

Percentile

##### Optimization using PORT routines

Unconstrained and box-constrained optimization using PORT routines. For historical compatibility.

Keywords
optimize
##### Usage
nlminb(start, objective, gradient = NULL, hessian = NULL, …,
scale = 1, control = list(), lower = -Inf, upper = Inf)
##### Arguments
start
numeric vector, initial values for the parameters to be optimized.
objective
Function to be minimized. Must return a scalar value. The first argument to objective is the vector of parameters to be optimized, whose initial values are supplied through start. Further arguments (fixed during the course of the optimization) to objective may be specified as well (see …).
Optional function that takes the same arguments as objective and evaluates the gradient of objective at its first argument. Must return a vector as long as start.
hessian
Optional function that takes the same arguments as objective and evaluates the hessian of objective at its first argument. Must return a square matrix of order length(start). Only the lower triangle is used.
Further arguments to be supplied to objective.
scale
See PORT documentation (or leave alone).
control
A list of control parameters. See below for details.
lower, upper
vectors of lower and upper bounds, replicated to be as long as start. If unspecified, all parameters are assumed to be unconstrained.
##### Details

Any names of start are passed on to objective and where applicable, gradient and hessian. The parameter vector will be coerced to double. The parameter vector passed to objective, gradient and hessian had special semantics prior to R 3.1.0 and was shared between calls. The functions should not copy it. If any of the functions returns NA or NaN the internal code could infinite-loop in R prior to 2.15.2: this is now an error for the gradient and Hessian, and such values for function evaluation are replaced by +Inf with a warning.

##### Value

A list with components:

par
The best set of parameters found.
objective
The value of objective corresponding to par.
convergence
An integer code. 0 indicates successful convergence.
message
A character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation.
iterations
Number of iterations performed.
evaluations
Number of objective function and gradient function evaluations

##### Control parameters

Possible names in the control list and their default values are:

eval.max
Maximum number of evaluations of the objective function allowed. Defaults to 200.
% MXFCAL
iter.max
Maximum number of iterations allowed. Defaults to 150.
% MXITER
trace
The value of the objective function and the parameters is printed every trace'th iteration. Defaults to 0 which indicates no trace information is to be printed.
abs.tol
Absolute tolerance. Defaults to 0 so the absolute convergence test is not used. If the objective function is known to be non-negative, the previous default of 1e-20 would be more appropriate.
% AFCTOL 31
rel.tol
Relative tolerance. Defaults to 1e-10.
% RFCTOL 32
x.tol
X tolerance. Defaults to 1.5e-8.
% XCTOL 33
xf.tol
false convergence tolerance. Defaults to 2.2e-14.
% XFTOL 34
step.min, step.max
Minimum and maximum step size. Both default to 1..
% LMAX0 35 / LMAXS 36
sing.tol
singular convergence tolerance; defaults to rel.tol.
% SCTOL 37
scale.init
...
% DINIT 38
diff.g
an estimated bound on the relative error in the objective function value.
% ETA0 42

##### References

David M. Gay (1990), Usage summary for selected optimization routines. Computing Science Technical Report 153, AT&T Bell Laboratories, Murray Hill.

optim (which is preferred) and nlm. optimize for one-dimensional minimization and constrOptim for constrained optimization.