Module optimizer 

Numerical optimizer for smoothing parameter estimation.

Implements the Nelder-Mead simplex algorithm (downhill simplex method) for unconstrained optimization of objective functions over low-dimensional parameter spaces (1–5 dimensions), which is the standard approach for exponential smoothing parameter estimation.

Box constraints

Parameters are internally transformed via a logit/sigmoid mapping to enforce box constraints (e.g. α ∈ (0, 1)) while the optimizer operates in unconstrained space.

References

• Nelder, J.A. & Mead, R. (1965). “A simplex method for function minimization.” The Computer Journal, 7(4), 308–313.
• Lagarias et al. (1998). “Convergence properties of the Nelder–Mead simplex method in low dimensions.” SIAM J. Optim., 9(1), 112–147.

Structs

Bound

A box constraint on a parameter.

OptResult

Result of an optimization run.

Functions

minimize_brent

Minimize a scalar function f(x) over [lo, hi] using Brent’s method.

minimize_nelder_mead

Minimize f over a bounded parameter space using Nelder-Mead.