rosenbrock_func {EmiR}

Rosenbrock Function

Description

Implementation of n-dimensional Rosenbrock function, with \(n \geq 2\).

Usage

rosenbrock_func(x)

Arguments

x

numeric or complex vector.

Details

On an n-dimensional domain it is defined by

\[f(\vec{x}) = \sum_{i=1}^{n-1} \left[ 100(x_{i+1}-x_{i}^2)^2 + (x_{i}-1)^2 \right],\]

and is usually evaluated on \(x_{i} \in [ -5, 10 ]\), for all \(i=1,...,n\). The function has one global minimum at \(f(\vec{x})=0\) for \(x_{i}=1\) for all \(i=1,...,n\).

Value

The value of the function.

References

Rosenbrock HH (1960). “An Automatic Method for Finding the Greatest or Least Value of a Function.” The Computer Journal, 3(3), 175–184. doi:10.1093/comjnl/3.3.175.