S3 neldermead object
Description
These functions support the S3 class 'neldermead'and are intended to either create objects of this class or check if an object is of this class.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  neldermead(optbase, method, simplex0, simplex0method,
simplex0length, simplexsize0, simplexopt, historysimplex, coords0, rho, chi,
gamma, sigma, tolfstdeviation, tolfstdeviationmethod, tolsimplexizeabsolute,
tolsimplexizerelative, tolsimplexizemethod, toldeltafv, tolssizedeltafvmethod,
simplex0deltausual, simplex0deltazero, restartsimplexmethod, restartmax,
restarteps, restartstep, restartnb, restartflag, restartdetection,
kelleystagnationflag, kelleynormalizationflag, kelleystagnationalpha0,
kelleyalpha, startupflag, boxnbpoints, boxnbpointseff, boxineqscaling,
checkcostfunction, scalingsimplex0, guinalphamin, boxboundsalpha,
boxtermination, boxtolf, boxnbmatch, boxkount, boxreflect, tolvarianceflag,
tolabsolutevariance, tolrelativevariance, variancesimplex0, mymethod,
myterminate, myterminateflag, greedy, output, exitflag)
## S3 method for class 'neldermead'
print(x,verbose,...)
## S3 method for class 'neldermead'
summary(object,showhistory,...)
## S3 method for class 'neldermead'
is(x=NULL)

Arguments
optbase 
An object of class 'optimbase', i.e. a list created by

method 
The name of the algorithm to use. 
simplex0 
An object of class 'simplex', i.e. a list created by

simplex0method 
The method to use to compute the initial simplex. 
simplex0length 
The length to use when the initial simplex is computed with the 'axes' or 'spendley' methods. 
rho 
The reflection coefficient. This parameter is used when the

chi 
The expansion coefficient. This parameter is used when the

gamma 
The contraction coefficient. This parameter is used when the

sigma 
The shrinkage coefficient. This parameter is used when the

tolfstdeviation 
The tolerance for the standard deviation. 
tolfstdeviationmethod 
Set to FALSE. 
tolsimplexizeabsolute 
The absolute tolerance on the simplex size. 
tolsimplexizerelative 
The relative tolerance on the simplex size. 
tolsimplexizemethod 
Logical flag to enable/disable the tolerance on
the simplex size. When this criteria is enabled, the values of the

simplexsize0 
Initial size of the simplex, for the tolerance on the simplex size. 
toldeltafv 
The absolute tolerance on the difference between the highest and the lowest function values. 
tolssizedeltafvmethod 
Logical flag to enable/disable the termination
criteria based on the size of the simplex and the difference of function
value in the simplex. If this criteria is triggered, the status of the
optimization is set to 'tolsizedeltafv'. This termination criteria uses
the values of the 
historysimplex 
The list to store the history for simplex. The simplex
will be stored on a new level of the list at each iteration, so the length
of 
coords0 
The coordinates of the vertices of the initial simplex. If
the 
simplex0deltausual 
The relative delta for nonzero parameters in 'pfeffer' method. 
simplex0deltazero 
The absolute delta for nonzero parameters in 'pfeffer' method. 
simplexopt 
The optimum simplex, after one optimization process. 
restartsimplexmethod 
The method to compute the initial simplex after a restart. 
restartmax 
The maximum number of restarts, when automatic restart is
enabled via the 
restarteps 
The absolute epsilon value used to check for optimality in the factorial O'Neill restart detection. 
restartstep 
The absolute step length used to check for optimality in the factorial O'Neill restart detection. 
kelleystagnationflag 
Logical flag to enable/disable the termination criteria using Kelley's stagnation detection, based on sufficient decrease condition. If this criteria is triggered, the status of the optimization is set to 'kelleystagnation'. 
,
kelleynormalizationflag 
Logical flag to enable/disable the
normalization of the alpha coefficient in Kelley's stagnation detection,
i.e. use the value of the 
kelleystagnationalpha0 
The parameter used in Kelley's stagnation detection. 
kelleyalpha 
The current value of Kelley's alpha, after normalization, if required. 
restartnb 
Number of restarts performed. 
restartflag 
Logical flag to enable/disable the automatic restart of the algorithm. 
restartdetection 
The method to detect if the automatic restart must be performed. 
startupflag 
Set to TRUE when the startup has been performed. 
boxnbpoints 
The number of points in the initial simplex, when the

boxnbpointseff 
The effective number of points required in the simplex for Box's algorithm. 
boxineqscaling 
The scaling coefficient used to scale the trial point for function improvement or into the constraints of Box's algorithm. 
checkcostfunction 
Logical flag to enable/disable the checking of the connection of the cost function. 
scalingsimplex0 
The algorithm used to scale the initial simplex into the nonlinear constraints. The following two algorithms are provided:
If the centroid happens to be unfeasible, because the constraints are not convex, the scaling of the initial simplex toward the centroid may fail. Since the initial guess is always feasible, scaling toward the initial guess cannot fail. 
guinalphamin 
The minimum value of alpha when scaling the vertices of the simplex into nonlinear constraints in Box's algorithm. 
boxboundsalpha 
The parameter used to project the vertices into the bounds in Box's algorithm. 
boxtermination 
Logical flag to enable/disable Box's termination criteria. 
boxtolf 
The absolute tolerance on difference of function values in
the simplex, suggested by Box. This tolerance is used if the

boxnbmatch 
The number of consecutive match of Box's termination criteria. 
boxkount 
Current number of consecutive match. 
boxreflect 
The reflection factor in Box's algorithm. 
tolvarianceflag 
Logical flag to enable/disable the termination criteria based on the variance of the function value. If this criteria is triggered, the status of the optimization is set to 'tolvariance'. This criteria is suggested by Nelder and Mead. 
tolabsolutevariance 
The absolute tolerance on the variance of the function values of the simplex. 
tolrelativevariance 
The relative tolerance on the variance of the function values of the simplex. 
variancesimplex0 
Relative tolerance on variance. 
mymethod 
A userderined simplex algorithm. 
myterminate 
A userdefined terminate function. 
myterminateflag 
Logical flag to enable/disable the userdefined terminate function. 
greedy 
Logical flag to enable/disable greedy NelderMead. 
output 
The command to call back for userdefined output of specialized function. 
exitflag 
Logical flag to enable/disable the userdefined output of specialized function. 
x 
An object of class 'neldermead'. 
verbose 
A logical flag, controlling the amount of data printed. 
... 
optional arguments to 'print' or 'plot' methods. 
object 
An object of class 'neldermead'. 
showhistory 
Optional logical flag, to define whether optimization history must be summarized or not. 
Value
The neldermead
function returns a new object of class 'neldermead',
with the following default content:
 optbase
An object of class 'optimbase' with the following default content:
 verbose
Default is FALSE.
 x0
Default is NULL.
 fx0
Default is NULL.
 xopt
Default is 0.
 fopt
Default is 0.
 tolfunabsolute
Default is 0.
 tolfunrelative
Default is .Machine$double.eps.
 tolfunmethod
Default is FALSE.
 tolxabsolute
Default is 0.
 tolxrelative
Default is .Machine$double.eps.
 tolxmethod
Default is TRUE.
 funevals
Default is 0.
 maxfunevals
Default is 100.
 maxiter
Default is 100.
 iterations
Default is 0.
 fun
Default is ”.
 status
Default is ”.
 historyfopt
Default is NULL.
 historyxopt
Default is NULL.
 verbosetermination
Default is FALSE.
 outputcommand
Default is ”.
 outputcommandarg
Default is ”. If the user configures this element, it is expected to be an object of class 'optimbase.outputargs' or will be coerced to an object of class 'optimbase.outputargs'.
 numberofvariables
Default is 0.
 storehistory
Default is FALSE.
 costfargument
Default is ”. If the user configures this element, it is expected to be an object of class 'optimbase.functionargs' or will be coerced to an object of class 'optimbase.functionargs'.
 boundsmin
Default is NULL.
 boundsmax
Default is NULL.
 nbineqconst
Default is 0.
 logfile
Default is ”.
 logfilehandle
Default is 0.
 logstartup
Default is FALSE.
 withderivatives
Default is FALSE.
 method
Default is 'variable'.
 simplex0
Default is an object of class 'simplex', with the following content:
 verbose
Default is 0.
 x
Default is NULL.
 n
Default is 0.
 fv
Default is NULL.
 nbve
Default is 0.
 simplex0method
Default is 'axes'.
 simplex0length
Default is 1.
 rho
Default is 1.
 chi
Default is 2.
 gamma
Default is 0.5.
 sigma
Default is 0.5.
 tolfstdeviation
Default is 0.
 tolfstdeviationmethod
Default is FALSE.
 tolsimplexizeabsolute
Default is 0.
 tolsimplexizerelative
Default is .Machine$double.eps.
 tolsimplexizemethod
Default is FALSE.
 simplexsize0
Default is 0.
 toldeltafv
Default is .Machine$double.eps.
 tolssizedeltafvmethod
Default is FALSE.
 historysimplex
Default is NULL.
 coords0
Default is NULL.
 simplex0deltausual
Default is 0.05.
 simplex0deltazero
Default is 0.0075.
 simplexopt
Default is NULL.
 restartsimplexmethod
Default is 'oriented'.
 restartmax
Default is 3.
 restarteps
Default is .Machine$double.eps.
 restartstep
Default is 1.
 kelleystagnationflag
Default is FALSE.
,
 kelleynormalizationflag
Default is TRUE, i.e. the simplex gradient of the initial simplex is taken into account in the stagnation detection.
 kelleystagnationalpha0
Default is 1.e4.
 kelleyalpha
Default is 1.e4.
 restartnb
Default is 0.
 restartflag
Default is FALSE.
 restartdetection
Default is 'oneill'.
 startupflag
Default is FALSE.
 boxnbpoints
Default is '2n'.
 boxnbpointseff
Default is 0.
 boxineqscaling
Default is 0.
 checkcostfunction
Default is TRUE.
 scalingsimplex0
Default is 'tox0'.
 guinalphamin
Default is 1.e6.
 boxtermination
Default is FALSE.
 boxtolf
Default is 1.e5.
 boxnbmatch
Default is 5.
 boxkount
Default is 0.
 boxreflect
Default is 1.3.
 tolvarianceflag
Default is FALSE.
 tolabsolutevariance
Default is 0.
 tolrelativevariance
Default is .Machine$double.eps.
 variancesimplex0
Default is .Machine$double.eps.
 mymethod
Default is NULL.
 myterminate
Default is NULL.
 myterminateflag
Default is FALSE.
 greedy
Default is FALSE.
 output
Default is list().
 exitflag
Default is FALSE.
Author(s)
Author of Scilab neldermead module: Michael Baudin (INRIA  Digiteo)
Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)
See Also
optimbase
,
optimsimplex