benchmarkfcns.powellsum

benchmarkfcns.powellsum(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 Powell Sum benchmark function. SCORES = powellsum(X) computes the value of the Powell Sum function at point X. powellsum 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: (0, 0, …, 0)

  • Number of dimensions: n (Scalable)

  • Recommended domain: x_i ∈ [-1, 1]

  • Number of local minima: 0

  • Number of global minima: 1

  • Convexity: Convex

  • Separability: Separable

  • Modality: Unimodal

  • Symmetry: Symmetric (relative to the origin)

  • Differentiable: Yes

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

Mathematical Definition

Visualization

powellsum landscape