benchmarkfcns.bentcigar

benchmarkfcns.bentcigar(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 Bent Cigar benchmark function. SCORES = bentcigar(X) computes the value of the Bent Cigar function at point X. bentcigar accepts a matrix of size M-by-N and returns a vetor SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • Global minimum: 0

  • Location of global minimum: (0, 0, …, 0)

  • Number of dimensions: n

  • Recommended domain: [-100, 100]^n

  • Modality: unimodal

  • Characteristic: Extreme ill-conditioning (10^6 scaling for all dimensions except the first).

Mathematical Definition

\[f(\mathbf{x}) = x_1^2 + 10^6 \sum_{i=2}^n x_i^2\]

Visualization

../_images/bentcigarfcn.png