benchmarkfcns.picheny

benchmarkfcns.picheny(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 Picheny benchmark function. SCORES = picheny(X) computes the value of the Picheny function at point X. picheny accepts a matrix of size M-by-2 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: -1.0 (approximately)

  • Location of global minimum: x ≈ 0.757

  • Number of dimensions: 1

  • Recommended domain: x ∈ [0, 1]

  • Number of local minima: Numerous (Highly oscillatory in specific regions)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Modality: Highly Multimodal

  • Differentiable: Yes

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

Mathematical Definition

Visualization

picheny landscape