benchmarkfcns.bukinn5

benchmarkfcns.bukinn5(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 Bukin N. 5 benchmark function. SCORES = bukinn5(X) computes the value of the function at point X. bukinn5 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 0

  • Location of global minimum: (-10, 1)

  • Number of dimensions: 2

  • Recommended domain: x1 in [-15, -5], x2 in [-3, 3]

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = 100(x_2 - 0.01x_1^2)^2 + 0.01 |x_1 + 10|\]

Visualization

../_images/bukinn5fcn.png