benchmarkfcns.pricen4

benchmarkfcns.pricen4(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 Price N. 4 benchmark function. SCORES = pricen4(X) computes the value of the Price N. 4 function at point X. pricen4 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: (0, 0), (2, 4), (1.4643, 2.5060)

  • Number of dimensions: 2

  • Recommended domain: [-500, 500]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = (2x_1^3 x_2 - x_2^3)^2 + (6x_1 - x_2^2 + x_2)^2\]

Visualization

../_images/pricen4fcn.png