benchmarkfcns.zettel

benchmarkfcns.zettel(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 Zettel function. SCORES = zettel(X) computes the value of the Zettel function at point X. zettel 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: -0.003791

  • Location of global minimum: (-0.02989, 0)

  • Number of dimensions: 2

  • Recommended domain: [-5, 5]^2

  • Number of local minima: 0 (It is unimodal)

  • Number of global minima: 1

  • Convexity: Non-convex (despite being unimodal, the “skew” makes it non-convex)

  • Separability: Non-separable (The x_1 and x_2 terms are combined inside the

    squared term)

  • Modality: Unimodal

  • Differentiable: Yes

Mathematical Definition

Visualization

zettel landscape