Optimization Toolbox (optim)

Unconstrained and bound-constrained nonlinear optimization, root finding (fzero, fsolve), and nonlinear curve fitting. More...

Files
file	fzero.hpp
	Scalar root-finding and unconstrained minimisation.

Functions
Value	nk::optim::fzero (FnHandle fn, double x0, std::pmr::memory_resource *mr=nullptr)
	Scalar root-finder, initial-guess form (x = fzero(fn, x0)).
Value	nk::optim::fzero (FnHandle fn, double a, double b, std::pmr::memory_resource *mr=nullptr)
	Scalar root-finder, bracket form (x = fzero(fn, a, b)).
Value	nk::optim::fminbnd (FnHandle fn, double lo, double hi, double tol, std::pmr::memory_resource *mr=nullptr)
	Bounded scalar minimisation (x = fminbnd(fn, lo, hi, tol)).
Value	nk::optim::fminsearch (FnHandle fn, Span< const double > x0, double tol, std::pmr::memory_resource *mr=nullptr)
	Multi-dimensional unconstrained minimisation (x = fminsearch(fn, x0, tol)).

Detailed Description

Unconstrained and bound-constrained nonlinear optimization, root finding (fzero, fsolve), and nonlinear curve fitting.

Function Documentation

fminbnd()

Value nk::optim::fminbnd	(	FnHandle	fn,
		double	lo,
		double	hi,
		double	tol,
		std::pmr::memory_resource *	mr = nullptr )

Bounded scalar minimisation (x = fminbnd(fn, lo, hi, tol)).

Brent's golden-section + parabolic-interpolation hybrid on [lo, hi].

Parameters

fn	Callback (scalar in, scalar out).
lo	Lower bound.
hi	Upper bound (hi > lo).
tol	Convergence tolerance on the minimiser location.
mr	Memory resource (nullptr → process default).

Returns

Scalar minimiser x* ∈ [lo, hi].

See also

fzero, fminsearch

fminsearch()

Value nk::optim::fminsearch	(	FnHandle	fn,
		Span< const double >	x0,
		double	tol,
		std::pmr::memory_resource *	mr = nullptr )

Multi-dimensional unconstrained minimisation (x = fminsearch(fn, x0, tol)).

Nelder-Mead simplex starting at x0. The callback receives a 1-element args whose [0] entry is a 1 × n DOUBLE row Value of length n = x0.size(), and writes a scalar into outs[0].

Parameters

fn	Callback (vector in, scalar out).
x0	Starting point (any length ≥ 1).
tol	Convergence tolerance.
mr	Memory resource (nullptr → process default).

Returns

Minimiser as a n × 1 DOUBLE column Value (length n = x0.size()).

See also

fminbnd

fzero() [1/2]

Value nk::optim::fzero	(	FnHandle	fn,
		double	a,
		double	b,
		std::pmr::memory_resource *	mr = nullptr )

Scalar root-finder, bracket form (x = fzero(fn, a, b)).

Runs Brent's method on [a, b]. Throws if sign(fn(a)) == sign(fn(b)) (no sign change inside the interval).

Parameters

fn	Callback (scalar in, scalar out).
a	Lower bracket bound (must be finite, a < b).
b	Upper bracket bound (must be finite, a < b).
mr	Memory resource (nullptr → process default).

Returns

Scalar root.

Exceptions

Error

No sign change in [a, b], or invalid bounds.

See also

fminbnd

fzero() [2/2]

Value nk::optim::fzero	(	FnHandle	fn,
		double	x0,
		std::pmr::memory_resource *	mr = nullptr )

Scalar root-finder, initial-guess form (x = fzero(fn, x0)).

Expands an outward bracket around x0 until a sign change is detected, then runs Brent's method.

The callback receives a 1-element args (the scalar evaluation point) and writes its scalar result into outs[0].

Parameters

fn	Callback (scalar in, scalar out).
x0	Initial guess.
mr	Memory resource (nullptr → process default).

Returns

Scalar root.

Exceptions

Error

No sign change found near x0.

See also

fminbnd