benchmarkfcns.qing

benchmarkfcns.qing(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 Qing function. SCORES = qing(X) computes the value of the Qing function at point X. qing accepts a matrix of size M-by-N 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: 0

  • Location of global minimum: x_i = pm sqrt{i}

  • Number of dimensions: n

  • Recommended domain: [-500, 500]^n

  • Number of local minima: many

  • Number of global minima: 2^n

  • Convexity: non-convex

  • Separability: separable

  • Modality: multimodal

  • Differentiable: Yes

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

Mathematical Definition

Visualization

qing landscape