benchmarkfcns.giunta

benchmarkfcns.giunta(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 Giunta function. SCORES = giunta(X) computes the value of the Giunta function at point X. giunta 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: approx 0.06447 (for n=2)

  • Location of Global Minimum: approx 0.46732

  • Number of Dimensions: Usually 2, but can be scaled to n dimensions

  • Recommended Domain: [-1, 1]^n

  • Number of Local Minima: Numerous (it oscillates rapidly)

  • Number of Global Minima: 1 (in the standard domain)

  • Convexity: Non-convex

  • Separability: Separable.

  • Modality: Multimodal

  • Symmetry: Symmetric (if all x_i ranges are the same)

  • Differentiable: Yes. It is smooth and continuous, unlike the Gear function.

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

Mathematical Definition

Visualization

giunta landscape