`neldermead`

package`neldermead`

is a R port of a module originally developed for Scilab version 5.2.1 by Michael Baudin (INRIA - DIGITEO). Information about this software can be found at www.scilab.org. The following documentation as well as the content of the functions .Rd files are adaptations of the documentation provided with the original Scilab neldermead module.

`neldermead`

currently does not include any adaptation of the Scilab ‘nmplot’ function series that is available in the original `neldermead`

module.

The goal of this toolbox is to provide several direct search optimization algorithms based on the simplex method. The optimization problem to solve is the minimization of a cost function, with bounds and nonlinear constraints.

\[ \begin{array}{l l} min f(x)\\ l_i \le{} x_i \le{} h_i, & i = 1,n \\ g_j(x) \ge{} 0, & j = 0,nb_{ineq} \\\\ \end{array} \]

where \(f\) is the cost function, \(x\) is the vector of parameter estimates, \(l\) and \(h\) are vectors of lower and upper bounds for the parameter estimates, \(n\) is the number of parameters and \(nb_{ineq}\) the number of inequality constraints \(g(x)\).

The provided algorithms are direct search algorithms, i.e. algorithms which do not use the derivative of the cost function. They are based on the update of a simplex, which is a set of \(k \ge n+1\) vertices, where each vertex is associated with one point and one function value.

The following algorithms are available:

- The fixed shape simplex method of Spendley, Hext and Himsworth: this algorithm solves an unconstrained optimization problem with a fixed shape simplex made of \(k = n+1\) vertices.
- The variable shape simplex method of Nelder and Mead: this algorithm solves an unconstrained optimization problem with a variable shape simple