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Minimisation: a bounded scalar minimiser and damped Gauss-Newton (Levenberg-Marquardt) for nonlinear least squares.
minimize_scalar: Brent’slocalmin(golden section with parabolic interpolation), Brent 1973 chapter 5, OCCTmath_BrentMinimum.levenberg_marquardt: minimises1/2 ||r(x)||^2with Moré’s column scaling (Moré, The Levenberg-Marquardt algorithm: implementation and theory, 1978) and Nielsen’s damping update. Each step solves the damped system as an augmented least-squares problem by QR rather than forming normal equations, so the Jacobian’s conditioning is not squared. A square system with a zero-residual solution makes this a solver for nonlinear equations (OCCTmath_FunctionSetRoot).
Both are local methods: they find a local minimiser near the start (or inside the bracket), and say how they stopped.
Structs§
- Least
Squares Minimum - A local minimiser of
1/2 ||r(x)||^2. - Levenberg
Marquardt Options - Stopping rules and budget for
levenberg_marquardt. - Scalar
Minimum - A local minimum of a scalar function on an interval.
Enums§
- Termination
- Why
levenberg_marquardtstopped.
Traits§
- Residuals
- A vector-valued residual function
r: R^n -> R^mforlevenberg_marquardt.
Functions§
- levenberg_
marquardt - Minimise
1/2 ||r(x)||^2fromx0by Levenberg-Marquardt. - minimize_
scalar - Minimise
fon[lower, upper]by Brent’s method.