colville_func {EmiR}

Colville Function

Description

Implementation of 4-dimensional Colville function.

Usage

colville_func(x)

Arguments

x

numeric or complex vector.

Details

On an 4-dimensional domain it is defined by

\[f(\vec{x}) = 100(x_1^2-x_2)^2+(x_1-1)^2+(x_3-1)^2+90(x_3^2-x_4)^2+10.1((x_2-1)^2+(x_4-1)^2)+19.8(x_2-1)(x_4-1),\]

and is usually evaluated on \(x_{i} \in [ -10, 10 ]\), for all \(i=1,...,4\). The function has one global minimum at \(f(\vec{x}) = 0\) for \(\vec{x} = [ 1, 1, 1, 1 ]\).

Value

The value of the function.

References

Grippo L, Lampariello F, Lucidi S (1989). “A truncated Newton method with nonmonotone line search for unconstrained optimization.” Journal of Optimization Theory and Applications, 60(3), 401–419. doi:10.1007/bf00940345.