benchmarkfcns.quartic

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

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

  • Global minimum: 0 (without noise)

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

  • Number of dimensions: n

  • Recommended domain: [-1.28, 1.28]^n

  • Number of local minima: 0 (unimodal, without noise)

  • Number of global minima: 1

  • Convexity: convex

  • Separability: separable

  • Modality: unimodal

  • Symmetry: symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/quarticfcn

Mathematical Definition

Visualization

quartic landscape