benchmarkfcns.powellsingular

benchmarkfcns.powellsingular(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Powell Singular benchmark function. SCORES = powellsingular(X) computes the value of the Powell Singular function at point X. powellsingular accepts a matrix of size M-by-4 and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

• Global minimum: 0

• Location of global minimum: (0, 0, 0, 0)

• Number of dimensions: 4

• Recommended domain: [-4, 5]^4

• Number of local minima: 0

• Number of global minima: 1

• Convexity: non-convex

• Separability: non-separable

• Modality: unimodal

Mathematical Definition

\[f(\mathbf{x}) = (x_1 + 10x_2)^2 + 5(x_3 - x_4)^2 + (x_2 - 2x_3)^4 + 10(x_1 - x_4)^4\]

Visualization

No visualization available for this function.