Package 'optimsimplex' reference manual

Title:	R Port of the 'Scilab' Optimsimplex Module
Description:	Provides a building block for optimization algorithms based on a simplex. The 'optimsimplex' package may be used in the following optimization methods: the simplex method of Spendley et al. (1962) <doi:10.1080/00401706.1962.10490033>, the method of Nelder and Mead (1965) <doi:10.1093/comjnl/7.4.308>, Box's algorithm for constrained optimization (1965) <doi:10.1093/comjnl/8.1.42>, the multi-dimensional search by Torczon (1989) <https://www.cs.wm.edu/~va/research/thesis.pdf>, etc...
Authors:	Sebastien Bihorel [aut, cre], Michael Baudin [aut]
Maintainer:	Sebastien Bihorel <[email protected]>
License:	CeCILL-2
Version:	1.0-8
Built:	2024-10-14 06:32:00 UTC
Source:	CRAN

R port of the Scilab optimsimplex module

Description

The goal of this package is to provide a building block for optimization algorithms based on a simplex. The optimsimplex package may be used in the following optimization methods:

the simplex method of Spendley et al.,
the method of Nelder and Mead,
the Box's algorithm for constrained optimization,
the multi-dimensional search by Torczon,
etc ...

Features The following is a list of features currently provided:

Manage various simplex initializations
- initial simplex given by user,
- initial simplex computed with a length and along the coordinate axes,
- initial regular simplex computed with Spendley et al. formula,
- initial simplex computed by a small perturbation around the initial guess point,
- initial simplex computed from randomized bounds.
sort the vertices by increasing function values,
compute the standard deviation of the function values in the simplex,
compute the simplex gradient with forward or centered differences,
shrink the simplex toward the best vertex,
etc...

Details

Package:	optimsimplex
Type:	Package
Version:	1.0-8
Date:	2022-01-28
License:	CeCILL-2
LazyLoad:	yes

See vignette('optimsimplex',package='optimsimplex') for more information.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Computation of Function Value(s)

Description

These functions compute the value of the function at the vertices points stored in the current simplex object and stored them back into the simplex object. optimsimplex.computefv determines how many vertices are stored in the simplex object and delegates the calculation of the function values to optimsimplex.compsomefv.

Usage

  optimsimplex.computefv(this = NULL, fun = NULL, data = NULL)
  optimsimplex.compsomefv(this = NULL, fun = NULL, indices = NULL, data = NULL)
optimsimplex.computefv(this = NULL, fun = NULL, data = NULL)
  optimsimplex.compsomefv(this = NULL, fun = NULL, indices = NULL, data = NULL)

Arguments

this

The current simplex object, containing the nbve x n matrix of vertice coordinates (i.e. x element), where n is the dimension of the space and nbve the number of vertices.

fun

The function to compute at vertices. The function is expected to have the following input and output arguments:

myfunction <- function(x, this){

...

return(list(f=f,this=this))

}

where x is a row vector and this a user-defined data, i.e. the data argument.

data

A user-defined data passed to the function. If data is provided, it is passed to the callback function both as an input and output argument. data may be used if the function uses some additionnal parameters. It is returned as an output parameter because the function may modify the data while computing the function value. This feature may be used, for example, to count the number of times that the function has been called.

indices

A vector of increasing integers from 1 to nbve.

Value

optimsimplex.computefv and optimsimplex.compsomefv return a list with the following elements:

this: The updated simplex object.
data: The updated user-defined data.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Optimsimplex Get Function Class

Description

The functions extract the content to various elements of a simplex object:

optimsimplex.getall: Get all the coordinates and the function values of all the vertices.
optimsimplex.getallfv: Get all the function values of all the vertices.
optimsimplex.getallx: Get all the coordinates of all the vertices.
optimsimplex.getfv: Get the function value at a given index.
optimsimplex.getn: Get the dimension of the space of the simplex.
optimsimplex.getnbve: Get the number of vertices of the simplex.
optimsimplex.getve: Get the vertex at a given index in the current simplex.
optimsimplex.getx: Get the coordinates of the vertex at a given index in the current simplex.

Usage

  optimsimplex.getall(this = NULL)
  optimsimplex.getallfv(this = NULL)
  optimsimplex.getallx(this = NULL)
  optimsimplex.getfv(this = NULL, ive = NULL)
  optimsimplex.getn(this = NULL)
  optimsimplex.getnbve(this = NULL)
  optimsimplex.getve(this = NULL, ive = NULL)
  optimsimplex.getx(this = NULL, ive = NULL)
optimsimplex.getall(this = NULL)
  optimsimplex.getallfv(this = NULL)
  optimsimplex.getallx(this = NULL)
  optimsimplex.getfv(this = NULL, ive = NULL)
  optimsimplex.getn(this = NULL)
  optimsimplex.getnbve(this = NULL)
  optimsimplex.getve(this = NULL, ive = NULL)
  optimsimplex.getx(this = NULL, ive = NULL)

Arguments

`this`	A simplex object.
`ive`	Vertex index.

Value

optimsimplex.getall

Return a nbve x n+1 matrix, where n is the dimension of the space, nbve is the number of vertices and with the following content:

simplex[k,1] is the function value of the vertex k, with k = 1 to nbve,
simplex[k,2:(n+1)] is the coordinates of the vertex k, with k = 1 to nbve.

optimsimplex.getallfv

Return a row vector of function values, which k^th element is the function value for the vertex k, with k = 1 to nbve.

optimsimplex.getallx

Return a nbve x n matrix of vertice coordinates; any given vertex is expected to be stored at row k, with k = 1 to nbve.

optimsimplex.getfv

Return a numeric scalar.

optimsimplex.getn

Return a numeric scalar.

optimsimplex.getnbve

Return a numeric scalar.

optimsimplex.getve

Return an object of class 'vertex', i.e. a list with the following elements:

n: The dimension of the space of the simplex.
x: The coordinates of the vertex at index ive.
fv: The value of the function at index ive.

optimsimplex.getx

Return a row vector, representing the coordinates of the vertex at index ive.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

S3 optimsimplex class

Description

These functions support the S3 class 'optimsimplex' and are intended to either create objects of this class or check if an object is of this class.

Usage

  optimsimplex(coords = NULL, fun = NULL, data = NULL, method = NULL,
               x0 = NULL, len = NULL, deltausual = NULL, deltazero = NULL,
               boundsmax = NULL, boundsmin = NULL, nbve = NULL,
               simplex0 = NULL)
  
  optimsimplex.tostring(x)
  
  ## S3 method for class 'optimsimplex'
print(x,...)
  
  ## S3 method for class 'optimsimplex'
is(x)
  
optimsimplex(coords = NULL, fun = NULL, data = NULL, method = NULL,
               x0 = NULL, len = NULL, deltausual = NULL, deltazero = NULL,
               boundsmax = NULL, boundsmin = NULL, nbve = NULL,
               simplex0 = NULL)
  
  optimsimplex.tostring(x)
  
  ## S3 method for class 'optimsimplex'
print(x,...)
  
  ## S3 method for class 'optimsimplex'
is(x)

Arguments

coords

The matrix of point estimate coordinates in the simplex. The coords matrix is expected to be a nbve x n matrix, where n is the dimension of the space and nbve is the number of vertices in the simplex, with nbve>= n+1. Only used if method is set to NULL.

fun

The function to compute at vertices. The function is expected to have the following input and output arguments:

myfunction <- function(x, this){

...

return(list(f=f,this=this))

}

where x is a row vector and this a user-defined data, i.e. the data argument.

data

method

The method used to create the new optimsimplex object, either 'axes', 'pfeffer', 'randbounds', 'spendley' or 'oriented'.

x0

The initial point estimates, as a row vector of length n.

len

The dimension of the simplex. If length is a value, that unique length is used in all directions. If length is a vector with n values, each length is used with the corresponding direction. Only used if method is set to 'axes' or 'spendley'.

deltausual

The absolute delta for non-zero values. Only used if method is set to 'pfeffer'.

deltazero

The absolute delta for zero values. Only used if method is set to 'pfeffer'.

boundsmin

A vector of minimum bounds. Only used if method is set to 'randbounds'.

boundsmax

A vector of maximum bounds. Only used if method is set to 'randbounds'.

nbve

The total number of vertices in the simplex. Only used if method is set to 'randbounds'.

simplex0

The initial simplex. Only used if method is set to 'oriented'.

x

An object of class 'optimsimplex'.

...

optional arguments to 'print' or 'plot' methods.

Details

All arguments of optimsimplex are optional. If no input is provided, the new optimsimplex object is empty.

If method is NULL, the new optimsimplex object is created by optimsimplex.coords. If coords is NULL, the optimsimplex object is empty; otherwise, coords is used as the initial vertice coordinates in the new simplex.

If method is set to 'axes', the initial vertice coordinates are stored in a nbve x n matrix built as follows:

[,1]	\|	x0[1]	....	x0[n]	\|		\|	len[1]	...	0	\|
[,.]	\|	...	...	...	\|	+	\|	...	...	...	\|
[,nbve]	\|	x0[1]	...	x0[n]	\|		\|	0	...	len[n]	\|

If method is set to 'pfeffer', the new optimsimplex object is created using the Pfeffer's method, i.e. a relative delta for non-zero values and an absolute delta for zero values.

If method is set to 'randbounds', the initial vertice coordinates are stored in a nbve x n matrix consisting of the initial point estimates (on the first row) and a (nbve-1) x n matrix of randomly sampled numbers between the specified the bounds. The number of vertices nbve in the optimsimplex is arbitrary.

If method is set to 'spendley', the new optimsimplex object is created using the Spendely's method, i.e. a regular simplex made of nbve = n+1 vertices.

If method is set to 'oriented', the new optimsimplex object is created in sorted order. The new simplex has the same sigma- length of the base simplex, but is "oriented" depending on the function value. The created optimsimplex may be used, as Kelley suggests, for a restart of Nelder-Mead algorithm.

The optimsimplex.tostring function is a utility function, which formats the content of a optimsimplex object into a single string of characters.

Value

The optimsimplex function returns a list with the following elements:

newobj

An object of class 'simplex', i.e. a list with the following elements:

verbose: The verbose option, controlling the amount of messages. Set to FALSE.
x: The coordinates of the vertices, with size nbve x n.
n: The dimension of the space.
fv: The values of the function at given vertices. It is a column matrix of length nbve.
nbve: The number of vertices.

data

The updated data input argument.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

References

"A Simplex Method for Function Minimization", Nelder, J. A. and Mead, R. The Computer Journal, January, 1965, 308-313

"Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation", W. Spendley, G. R. Hext, F. R. Himsworth, Technometrics, Vol. 4, No. 4 (Nov., 1962), pp. 441-461, Section 3.1

"A New Method of Constrained Optimization and a Comparison With Other Methods", M. J. Box, The Computer Journal 1965 8(1):42-52, 1965 by British Computer Society

"Detection and Remediation of Stagnation in the Nelder-Mead Algorithm Using a Sufficient Decrease Condition", SIAM J. on Optimization, Kelley C.T., 1999

"Multi-Directional Search: A Direct Search Algorithm for Parallel Machines", by E. Boyd, Kenneth W. Kennedy, Richard A. Tapia, Virginia Joanne Torczon, Virginia Joanne Torczon, 1989, Phd Thesis, Rice University

"Grid Restrained Nelder-Mead Algorithm", Arpad Burmen, Janez Puhan, Tadej Tuma, Computational Optimization and Applications, Volume 34 , Issue 3 (July 2006), Pages: 359 - 375

"A convergent variant of the Nelder-Mead algorithm", C. J. Price, I. D. Coope, D. Byatt, Journal of Optimization Theory and Applications, Volume 113 , Issue 1 (April 2002), Pages: 5 - 19,

"Global Optimization Of Lennard-Jones Atomic Clusters", Ellen Fan, Thesis, February 26, 2002, McMaster University

Examples

  myfun <- function(x,this){return(list(f=sum(x^2),this=this))}
  mat <- matrix(c(0,1,0,0,0,1),ncol=2)
  
  optimsimplex()
  optimsimplex(coords=mat,x0=1:4,fun=myfun)
  optimsimplex(method='axes',x0=1:4,fun=myfun)
  optimsimplex(method='pfeffer',x0=1:6,fun=myfun)
  opt <- optimsimplex(method='randbounds',x0=1:6,boundsmin=rep(0,6),
                          boundsmax=rep(10,6),fun=myfun)
  opt
  optimsimplex(method='spendley',x0=1:6,fun=myfun,len=10)
  optimsimplex(method='oriented',simplex=opt$newobj,fun=myfun)
 
myfun <- function(x,this){return(list(f=sum(x^2),this=this))}
  mat <- matrix(c(0,1,0,0,0,1),ncol=2)
  
  optimsimplex()
  optimsimplex(coords=mat,x0=1:4,fun=myfun)
  optimsimplex(method='axes',x0=1:4,fun=myfun)
  optimsimplex(method='pfeffer',x0=1:6,fun=myfun)
  opt <- optimsimplex(method='randbounds',x0=1:6,boundsmin=rep(0,6),
                          boundsmax=rep(10,6),fun=myfun)
  opt
  optimsimplex(method='spendley',x0=1:6,fun=myfun,len=10)
  optimsimplex(method='oriented',simplex=opt$newobj,fun=myfun)

Erase Simplex Object

Description

This function erases the coordinates of the vertices (x) and the function values (fv) in a simplex object

Usage

  optimsimplex.destroy(this = NULL)
optimsimplex.destroy(this = NULL)

Arguments

this

A simplex object.

Value

Return an updated simplex object for which the content of the x and fv elements were set to NULL.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Optimsimplex Logging

Description

This function prints a message to screen (or log file).

Usage

  optimsimplex.log(this = NULL, msg = NULL)
optimsimplex.log(this = NULL, msg = NULL)

Arguments

`this`	An simplex object.
`msg`	A message to print.

Value

Do not return any value but print msg to screen if the verbose in this is set to 1.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Simplex Reflection

Description

This function returns a new simplex by reflection of the current simplex with respect to the first vertex in the simplex. This move is used in the centered simplex gradient.

Usage

  optimsimplex.reflect(this = NULL, fun = NULL, data = NULL)
optimsimplex.reflect(this = NULL, fun = NULL, data = NULL)

Arguments

this

An simplex object.

fun

The function to compute at vertices. The function is expected to have the following input and output arguments:

myfunction <- function(x, this){

...

return(list(f=f,this=this))

}

where x is a row vector and this a user-defined data, i.e. the data argument.

data

Value

Return a list with the following elements:

r: The reflected simplex object.
data: The updated user-defined data.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Simplex Shrink

Description

This function shrinks the simplex with given coefficient sigma and returns an updated simplex. The shrink is performed with respect to the first point in the simplex.

Usage

  optimsimplex.shrink(this = NULL, fun = NULL, sigma = 0.5, data = NULL)
optimsimplex.shrink(this = NULL, fun = NULL, sigma = 0.5, data = NULL)

Arguments

this

An simplex object

fun

The function to compute at vertices. The function is expected to have the following input and output arguments:

myfunction <- function(x, this){

...

return(list(f=f,this=this))

}

where x is a row vector and this a user-defined data, i.e. the data.

sigma

The shrinkage coefficient. The default value is 0.5.

data

Value

Return a list with the following elements:

this: The updated simplex object.
data: The updated user-defined data.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Optimsimplex Utility Functions

Description

These functions enable various calculations and checks on the current simplex:

optimsimplex.center: Compute the center of the current simplex.
optimsimplex.check: Check the consistency of the data in the current simplex.
optimsimplex.deltafv: Compute the vector of function value differences with respect to the function value at the first vertex (the lowest).
optimsimplex.deltafvmax: Compute the difference of function value between the lowest and the highest vertices. It is expected that the first vertex (this$x[1,]) is associated with the smallest function value and that the last vertex (this$x[nbve,]) is associated with the highest function value.
optimsimplex.dirmat: Compute the matrix of simplex direction, i.e. the matrix of differences of vertice coordinates with respect to the first vertex.
optimsimplex.fvmean: Compute the mean of the function values in the current simplex.
optimsimplex.fvstdev: Compute the standard deviation of the function values in the current simplex.
optimsimplex.fvvariance: Compute the variance of the function values in the current simplex.
optimsimplex.size: Determines the size of the simplex.
optimsimplex.sort: Sort the simplex by increasing order of function value, so the smallest function is at the first vertex.
optimsimplex.xbar: Compute the center of n vertices, by excluding the vertex with index iexcl. The default of iexcl is the number of vertices: in that case, if the simplex is sorted in increasing function value order, the worst vertex is excluded.

Usage

  optimsimplex.center(this = NULL)
  optimsimplex.check(this = NULL)
  optimsimplex.deltafv(this = NULL)
  optimsimplex.deltafvmax(this = NULL)
  optimsimplex.dirmat(this = NULL)
  optimsimplex.fvmean(this = NULL)
  optimsimplex.fvstdev(this = NULL)
  optimsimplex.fvvariance(this = NULL)
  optimsimplex.size(this = NULL, method = NULL)
  optimsimplex.sort(this = NULL)
  optimsimplex.xbar(this = NULL, iexcl = NULL)
optimsimplex.center(this = NULL)
  optimsimplex.check(this = NULL)
  optimsimplex.deltafv(this = NULL)
  optimsimplex.deltafvmax(this = NULL)
  optimsimplex.dirmat(this = NULL)
  optimsimplex.fvmean(this = NULL)
  optimsimplex.fvstdev(this = NULL)
  optimsimplex.fvvariance(this = NULL)
  optimsimplex.size(this = NULL, method = NULL)
  optimsimplex.sort(this = NULL)
  optimsimplex.xbar(this = NULL, iexcl = NULL)

Arguments

this

The current simplex.

method

The method to use to compute the size of the simplex. The available methods are the following:

'sigmaplus': (this is the default) The sigmamplus size is the maximum 2-norm length of the vector from each vertex to the first vertex. It requires one loop over the vertices.
'sigmaminus': The sigmaminus size is the minimum 2-norm length of the vector from each vertex to the first vertex. It requires one loop over the vertices.
'Nash': The 'Nash' size is the sum of the norm of the norm-1 length of the vector from the given vertex to the first vertex. It requires one loop over the vertices.
'diameter': The diameter is the maximum norm-2 length of all the edges of the simplex. It requires 2 nested loops over the vertices.

iexcl

The index of the vertex to exclude in center computation.

Value

optimsimplex.center: Return a vector of length nbve, where nbve is the number of vertices in the current simplex.
optimsimplex.check: Return an error message if the dimensions of the various elements of the current simplex do not match.
optimsimplex.deltafv: Return a column vector of length nbve-1.
optimsimplex.deltafvmax: Return a numeric scalar.
optimsimplex.dirmat: Return a n x n numeric matrix, where n is the dimension of the space of the simplex.
optimsimplex.fvmean: Return a numeric scalar.
optimsimplex.fvstdev: Return a numeric scalar.
optimsimplex.fvvariance: Return a numeric scalar.
optimsimplex.size: Return a numeric scalar.
optimsimplex.sort: Return an updated simplex object.
optimsimplex.xbar: Return a row vector of length n.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

References

"Compact Numerical Methods For Computers - Linear Algebra and Function Minimization", J.C. Nash, 1990, Chapter 14. Direct Search Methods

"Iterative Methods for Optimization", C.T. Kelley, 1999, Chapter 6., section 6.2

S3 osimplex and vertex classes

Description

These functions support the S3 classes 'osimplex' and 'vertex'. They are intended to either create objects of these classes or check if an object is of these classes

Usage

  osimplex(verbose,x,n,fv,nbve)
  
  vertex(x,n,fv)
  
  ## S3 method for class 'osimplex'
print(x,...)
  
  ## S3 method for class 'vertex'
print(x,...)
  
  ## S3 method for class 'osimplex'
is(x)
  
  ## S3 method for class 'vertex'
is(x)
osimplex(verbose,x,n,fv,nbve)
  
  vertex(x,n,fv)
  
  ## S3 method for class 'osimplex'
print(x,...)
  
  ## S3 method for class 'vertex'
print(x,...)
  
  ## S3 method for class 'osimplex'
is(x)
  
  ## S3 method for class 'vertex'
is(x)

Arguments

`verbose`	The verbose option, controlling the amount of messages
`x`	The coordinates of the vertices, with size nbve x n in a simplex object or 1 x n in a vertex.
`n`	The dimension of the space.
`fv`	The values of the function at given vertices. It is a column matrix of length nbve in a simplex or a single value in a vertex.
`nbve`	The number of vertices in a simplex.
`...`	optional arguments to 'print' or 'plot' methods.

Details

A simplex of size n x nbve is essentially a collection of vertex of size n.

Value

osimplex returns a list with the following elements: verbose, x, n, fv, and nbve. vertex returns a list with the following elements: x, n, and fv.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Optimsimplex Set Function Class

Description

The functions assign content to various elements of a simplex object:

optimsimplex.setall: Set all the coordinates and the function values of all the vertices.
optimsimplex.setallfv: Set all the function values of all the vertices.
optimsimplex.setallx: Set all the coordinates of all the vertices.
optimsimplex.setfv: Set the function value at a givenindex.
optimsimplex.setn: Set the dimension of the space of the simplex.
optimsimplex.setnbve: Set the number of vertices of the simplex.
optimsimplex.setve: Set the coordinates of the vertex and the function values at a given index in the current simplex.
optimsimplex.setx: Set the coordinates of the vertex at a given index in the current simplex.

Usage

  optimsimplex.setall(this = NULL, simplex = NULL)
  optimsimplex.setallfv(this = NULL, fv = NULL)
  optimsimplex.setallx(this = NULL, x = NULL)
  optimsimplex.setfv(this = NULL, ive = NULL, fv = NULL)
  optimsimplex.setn(this = NULL, n = NULL)
  optimsimplex.setnbve(this = NULL, nbve = NULL)
  optimsimplex.setve(this = NULL, ive = NULL, fv = NULL, x = NULL)
  optimsimplex.setx(this = NULL, ive = NULL, x = NULL)
optimsimplex.setall(this = NULL, simplex = NULL)
  optimsimplex.setallfv(this = NULL, fv = NULL)
  optimsimplex.setallx(this = NULL, x = NULL)
  optimsimplex.setfv(this = NULL, ive = NULL, fv = NULL)
  optimsimplex.setn(this = NULL, n = NULL)
  optimsimplex.setnbve(this = NULL, nbve = NULL)
  optimsimplex.setve(this = NULL, ive = NULL, fv = NULL, x = NULL)
  optimsimplex.setx(this = NULL, ive = NULL, x = NULL)

Arguments

`this`	A simplex object.
`simplex`	The simplex to set. It is expected to be a nbve x n+1 matrix where n is the dimension of the space, nbve is the number of vertices and with the following content: `simplex[k,1]` is the function value of the vertex k, with k = 1 to nbve, `simplex[k,2:(n+1)]` is the coordinates of the vertex k, with k = 1 to nbve.
`fv`	A row vector of function values; `fv[k]` is expected to be the function value for the vertex k, with k = 1 to nbve. For `optimsimplex.setfv`, `fv` is expected to be a numerical scalar.
`x`	The nbve x n matrix of vertice coordinates; the vertex is expected to be stored in `x[k,1:n]`, with k = 1 to nbve. For `optimsimplex.setve` and `optimsimplex.setx`, `x` is expected to be a row matrix.
`ive`	Vertex index.
`n`	The dimension of the space of the simplex.
`nbve`	The number of vertices of the simplex.

Value

Return a updated simplex object this.

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Simplex Gradient

Description

optimsimplex.gradientfv determines the simplex gradient of the function which is computed by the secondary functions optimsimplex.gradcenter and optimsimplex.gradforward.

Usage

  optimsimplex.gradientfv(this = NULL, fun = NULL, method = "forward",
                          data = NULL)
  optimsimplex.gradcenter(this = NULL, fun = NULL, data = NULL)
  optimsimplex.gradforward(this = NULL)
optimsimplex.gradientfv(this = NULL, fun = NULL, method = "forward",
                          data = NULL)
  optimsimplex.gradcenter(this = NULL, fun = NULL, data = NULL)
  optimsimplex.gradforward(this = NULL)

Arguments

this

An simplex object

fun

The function to compute at vertices. The function is expected to have the following input and output arguments:

myfunction <- function(x, this){

...

return(list(f=f,this=this))

}

where x is a row vector and this a user-defined data, i.e. the data argument.

method

The method used to compute the simplex gradient. Two methods are available: 'forward' and 'centered'. The 'forward' method uses the current simplex to compute the gradient (using optimsimplex.dirmat and optimsimplex.deltafv). The 'centered' method creates an intermediate simplex and computes the average.

data

Value

optimsimplex.gradientfv returns a list with the following elements:

g: A column vector of function gradient (with length this$n).
data: The updated user-defined data.

optimsimplex.gradcenter returns a list with the following elements:

g: A column vector of function gradient (with length this$n).
data: The updated user-defined data.

optimsimplex.gradforward returns a column vector of function gradient (with length this$n).

Author(s)

Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel ([email protected])

Package 'optimsimplex'

Help Index

R port of the Scilab optimsimplex module

Description

Details

Author(s)

Computation of Function Value(s)

Description

Usage

Arguments

Value

Author(s)

See Also

Optimsimplex Get Function Class

Description

Usage

Arguments

Value

Author(s)

See Also

S3 optimsimplex class

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Erase Simplex Object

Description

Usage

Arguments

Value

Author(s)

See Also

Optimsimplex Logging

Description

Usage

Arguments

Value

Author(s)

See Also

Simplex Reflection

Description

Usage

Arguments

Value

Author(s)

See Also

Simplex Shrink

Description

Usage

Arguments

Value

Author(s)

See Also

Optimsimplex Utility Functions

Description

Usage

Arguments

Value

Author(s)

References

See Also

S3 osimplex and vertex classes

Description

Usage

Arguments

Details

Value

Author(s)

Optimsimplex Set Function Class

Description

Usage

Arguments

Value

Author(s)

See Also

Simplex Gradient