benchmarkfcns.cosinemixture

benchmarkfcns.cosinemixture(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 Cosine Mixture benchmark function. SCORES = cosinemixture(X) computes the value of the Cosine Mixture function at point X. cosinemixture 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 the corresponding row of X. Properties:

  • Global minimum: 0

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

  • Number of dimensions: n

  • Recommended domain: [-1, 1]^n

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: separable

  • Modality: multimodal

  • Symmetry: symmetric

  • Differentiable: Yes

Mathematical Definition

Visualization

cosinemixture landscape