optimsimplex.utils {optimsimplex}

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)

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 ([e-mail])

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

See Also

optimsimplex