benchmarkfcns.amgm

benchmarkfcns.amgm(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 AMGM benchmark function. SCORES = amgm(X) computes the value of the AMGM function at point X. amgm 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: 1

  • Location of global minimum: (x, x, …, x) for any x > 0

  • Number of dimensions: n

  • Recommended domain: (0, 10]^n (for non-negative inputs)

  • Number of local minima: 0 (unimodal)

  • Number of global minima: Infinite (along the line x_1 = x_2 = … = x_n)

  • Convexity: non-convex

  • Separability: non-separable

  • Symmetry: symmetric

  • Modality: unimodal (on the positive domain)

  • Differentiable: Yes

Mathematical Definition

Visualization

amgm landscape