benchmarkfcns.mccormick

benchmarkfcns.mccormick(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 McCormick benchmark function. SCORES = mccormick(X) computes the value of the McCormick function at point X. mccormick 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: -1.9133 (approximately)

  • Location of global minimum: (-0.54719, -1.54719)

  • Number of dimensions: 2

  • Recommended domain: x ∈ [-1.5, 4], y ∈ [-3, 4]

  • Number of local minima: 1

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Non-separable

  • Modality: Multimodal (Mildly)

  • Symmetry: Non-symmetric

  • Differentiable: Yes

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

Mathematical Definition

Visualization

mccormick landscape