benchmarkfcns.csendes

benchmarkfcns.csendes(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 Csendes benchmark function. SCORES = csendes(X) computes the value of the Csendes function at point X. csendes 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: convex (for x!= 0)

  • Separability: separable

  • Modality: unimodal

  • Differentiability: No (Technically, the derivative at x=0 is undefined or zero

    in a way that causes numerical instability in most solvers)

  • Symmetry: symmetric

Mathematical Definition

Visualization

csendes landscape