benchmarkfcns.beale

benchmarkfcns.beale(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 Beale benchmark function. SCORES = beale(X) computes the value of the Beale function at point X. beale accepts a matrix of size M-by-2 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: (3, 0.5)

  • Number of dimensions: 2

  • Recommended domain: [-4.5, 4.5]^2

  • Number of local minima: One global minimum in the standard domain, but it

    features several very flat regions that act like “pseudo-local minima” where gradients become nearly zero.

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Non-separable. The x and y variables are heavily multiplied and

    nested within the terms.

  • Modality: Unimodal (within its standard range), but deceptively difficult due

    to its geometry.

  • Symmetry: Non-symmetric

  • Differentiable: Yes

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

Mathematical Definition

Visualization

beale landscape