benchmarkfcns.adjiman

benchmarkfcns.adjiman(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 Adjiman benchmark function. SCORES = adjiman(X) computes the value of the Adjiman function at point X. adjiman 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: -2.02181 (approximately)

  • Location of global minimum: (2, 0.10578)

  • Number of dimensions: 2

  • Recommended domain: x_1 ∈ [-1, 2], x_2 ∈ [-1, 1]

  • Number of local minima: 0 (within the standard recommended domain, it is

    technically unimodal, though it has very flat regions)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Non-separable (The x_1 and x_2 terms are multiplied in the cosine

    and linear terms)

  • Modality: Unimodal

  • Symmetry: Non-symmetric

  • Differentiable: Yes

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

Mathematical Definition

Visualization

adjiman landscape