benchmarkfcns.langermann

benchmarkfcns.langermann(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 Langermann benchmark function. SCORES = langermann(X) computes the value of the Langermann function at point X. langermann 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: approx -5.1621259

  • Location of global minimum: approx (2.002992, 1.006096)

  • Number of dimensions: 2

  • Recommended domain: [0, 10]^2

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

Mathematical Definition

Visualization

langermann landscape