pbat::math::optimization::Newton< TScalar > Struct Template Reference

Newton's method for optimization. More...

#include <Newton.h>

Public Member Functions
	Newton (int nMaxIters=10, TScalar gtol=TScalar(1e-4), Index n=0)
	Construct a new Newton optimizer.
template<class FPrepareDerivatives, class FObjective, class FGradient, class FHessianInverseProduct, class TDerivedX>
TScalar	Solve (FPrepareDerivatives prepareDerivatives, FObjective f, FGradient g, FHessianInverseProduct Hinv, Eigen::MatrixBase< TDerivedX > &xk, std::optional< BackTrackingLineSearch< TScalar > > lineSearch=std::nullopt)
	Solve the optimization problem using Newton's method.

Public Attributes
int	nMaxIters
	Maximum number of iterations for the Newton solver.
TScalar	gtol2
	Gradient squared norm threshold for convergence.
Eigen::Vector< TScalar, Eigen::Dynamic >	dxk
	Step direction.
Eigen::Vector< TScalar, Eigen::Dynamic >	gk
	Gradient at current iteration.

Detailed Description

template<class TScalar = Scalar>
struct pbat::math::optimization::Newton< TScalar >

Newton's method for optimization.

Template Parameters

TScalar

Scalar type

Constructor & Destructor Documentation

Newton()

template<class TScalar>

pbat::math::optimization::Newton< TScalar >::Newton ( int nMaxIters = 10, TScalar gtol = TScalar(1e-4), Index n = 0 )

inline

Construct a new Newton optimizer.

Parameters

nMaxIters	Maximum number of iterations for the Newton solver
gtol	Gradient norm threshold for convergence
n	Number of degrees of freedom

Member Function Documentation

Solve()

template<class TScalar>

template<class FPrepareDerivatives, class FObjective, class FGradient, class FHessianInverseProduct, class TDerivedX>

TScalar pbat::math::optimization::Newton< TScalar >::Solve ( FPrepareDerivatives prepareDerivatives, FObjective f, FGradient g, FHessianInverseProduct Hinv, Eigen::MatrixBase< TDerivedX > & xk, std::optional< BackTrackingLineSearch< TScalar > > lineSearch = std::nullopt )

inline

Solve the optimization problem using Newton's method.

Template Parameters

FPrepareDerivatives	Callable type with signature prepareDerivatives(xk) -> void
FObjective	Callable type for the objective function with signature f(xk) -> fk
FGradient	Callable type for the gradient with signature g(xk) -> gk
FHessianInverseProduct	Callable type for the Hessian inverse product with signature Hinv(xk, gk) -> dxk
TDerivedX	Derived type for the input iterate

Parameters

prepareDerivatives	Derivative (pre)computation function
f	Objective function
g	Gradient function
Hinv	Hessian inverse product function
xk	Current iterate
lineSearch	Optional line search object

Returns

Squared norm of the gradient at the final iterate

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The documentation for this struct was generated from the following file:

• C:/git/PhysicsBasedAnimationToolkit/source/pbat/math/optimization/Newton.h