miele_cantrell_func {EmiR}

Miele Cantrell Function

Description

Implementation of 4-dimensional Miele Cantrell Function.

Usage

miele_cantrell_func(x)

Arguments

x

numeric or complex vector.

Details

On an 4-dimensional domain it is defined by

\[f(\vec{x}) = \left(e^{-x_{1}} - x_{2} \right)^4 + 100(x_{2} - x_{3})^6 + \left(\tan(x_{3} - x_{4})\right)^4 + x_{1}^8\]

and is usually evaluated on \(x_{i} \in [ -2, 2 ]\), for all \(i=1,...,4\). The function has one global minimum at \(f(\vec{x}) = 0\) for \(\vec{x} = [ 0, 1, 1, 1 ]\).

Value

The value of the function.

References

Cragg EE, Levy AV (1969). “Study on a supermemory gradient method for the minimization of functions.” Journal of Optimization Theory and Applications, 4(3), 191–205.