benchmarkfcns.alpinen1

benchmarkfcns.alpinen1(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 Alpine N. 1 function. SCORES = alpine1(X) computes the value of the Alpine N. 1 function at point X. alpine1 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

  • Recommended domain: [-10, 10]^n

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: separable

  • Modality: multimodal

  • Differentiable: Yes (except at points where sin(x_i) + 0.1 is 0, due to

    absolute value)

For more information, please visit: benchmarkfcns.info/doc/alpinen1fcn

Mathematical Definition

Visualization

alpinen1 landscape