benchmarkfcns.multifidelity.rosenbrock

benchmarkfcns.multifidelity.rosenbrock(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the multi-fidelity Rosenbrock benchmark function. SCORES = rosenbrock(X) computes the value of the Rosenbrock function at point X. multifidelity.rosenbrock accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2 in which each row contains the function value for the corresponding row of X and each column contains the function value for the corresponding fidelity level. Properties (High-fidelity):

  • Global minimum: 0

  • Location of global minimum: (1, 1, …, 1)

  • Number of dimensions: n

  • Recommended domain: [-5, 5]^n

  • Number of local minima: many (the “banana-shaped” valley creates a long, narrow region of local minima)

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: unimodal

  • Symmetry: non-symmetric

  • Differentiable: Yes

For more information, please visit: arxiv.org/pdf/2204.07867

Mathematical Definition

Visualization

rosenbrock landscape