benchmarkfcns.ridge

benchmarkfcns.ridge(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], d: SupportsFloat | SupportsIndex = 1, alpha: SupportsFloat | SupportsIndex = 0.5) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Ridge benchmark function. SCORES = ridge(X) computes the value of the Ridge function at point X. ridge 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. SCORES = ridge(X, d=D) specifies contribution coefficient of the sphere component of the function. SCORES = ridge(X, d=D, alpha=ALPHA) specifies power of the sphere component of the function. Properties:

  • Global minimum: depends on domain (usually at the boundary)

  • Location of global minimum: depends on domain

  • Number of dimensions: n

  • Recommended domain: [-5, 5]^n

  • Number of local minima: 0 (unimodal)

  • Number of global minima: 1

  • Convexity: convex

  • Separability: non-separable

  • Modality: unimodal

  • Differentiable: Yes (for alpha > 0.5)

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

Mathematical Definition

Visualization

ridge landscape