benchmarkfcns.treccani

benchmarkfcns.treccani(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 Treccani benchmark function. SCORES = treccani(X) computes the value of the Treccani function at point X. treccani 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

  • Location of global minimum: (0, 0), (-2, 0)

  • Number of dimensions: 2

  • Recommended domain: [-5, 5]^2

  • Number of local minima: 0 (The valleys lead to global minima)

  • Number of global minima: 2

  • Convexity: non-convex

  • Separability: separable

  • Modality: multimodal

  • Symmetry: symmetric

  • Differentiable: Yes

Mathematical Definition

Visualization

treccani landscape