MathOpt_Newton.hxx File Reference

#include <MathUtils_Types.hxx>
#include <MathUtils_Config.hxx>
#include <MathLin_Gauss.hxx>
#include <MathUtils_Core.hxx>
#include <MathUtils_LineSearch.hxx>
#include <MathUtils_Deriv.hxx>
#include <cmath>

Data Structures
struct	MathOpt::NewtonConfig
	Configuration for Newton minimization with Hessian. More...

Namespaces
namespace	MathOpt
	Optimization algorithms for scalar and vector functions.

Functions
template<typename Function >
VectorResult	MathOpt::Newton (Function &theFunc, const math_Vector &theStartingPoint, const NewtonConfig &theConfig=NewtonConfig())
	Newton's method for N-dimensional minimization using Hessian.
template<typename Function >
VectorResult	MathOpt::NewtonModified (Function &theFunc, const math_Vector &theStartingPoint, const NewtonConfig &theConfig=NewtonConfig())
	Modified Newton's method with automatic Hessian regularization. Adds diagonal elements to ensure positive definiteness using an adaptive regularization strategy.
template<typename Function >
VectorResult	MathOpt::NewtonNumericalHessian (Function &theFunc, const math_Vector &theStartingPoint, double theHessStep=1.0e-6, const NewtonConfig &theConfig=NewtonConfig())
	Newton's method with numerical Hessian. Computes Hessian using finite differences when analytical Hessian is not available.
template<typename Function >
VectorResult	MathOpt::NewtonNumerical (Function &theFunc, const math_Vector &theStartingPoint, double theGradStep=1.0e-8, double theHessStep=1.0e-6, const NewtonConfig &theConfig=NewtonConfig())
	Newton's method with fully numerical derivatives. Computes both gradient and Hessian using finite differences.
template<typename Function >
VectorResult	MathOpt::NewtonBounded (Function &theFunc, const math_Vector &theStartingPoint, const math_Vector &theLowerBounds, const math_Vector &theUpperBounds, const NewtonConfig &theConfig=NewtonConfig())
	Newton's method with bound constraints.