Nonlinear system solvers, unconstrained and constrained optimization methods, and benchmark test functions. More...

Classes
struct	minitensor::Function_Base< FunctionDerived, S, M >

struct	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >

struct	minitensor::Inequality_Constraint< ConstraintDerived, S, NC, NV >

struct	minitensor::Bounds< T, N >

struct	minitensor::Minimizer< T, N >

struct	minitensor::NewtonLineSearch< T, N >

struct	minitensor::BacktrackingLineSearch< T, N >

struct	minitensor::TrustRegionSubproblemBase< T, N >

struct	minitensor::TrustRegionExactValue< T, N >

struct	minitensor::TrustRegionExactGradient< T, N >

struct	minitensor::TrustRegionDogLegValue< T, N >

struct	minitensor::TrustRegionDogLegGradient< T, N >

struct	minitensor::StepBase< FN, T, N >

struct	minitensor::NewtonStep< FN, T, N >

struct	minitensor::NewtonWithLineSearchStep< FN, T, N >

struct	minitensor::TrustRegionStep< FN, T, N >

struct	minitensor::ConjugateGradientStep< FN, T, N >

struct	minitensor::LineSearchRegularizedStep< FN, T, N >

class	minitensor::SquareRoot< S, M >

class	minitensor::Quadratic< S, M >

class	minitensor::Gaussian< S, M >

class	minitensor::Banana< S, M >

class	minitensor::Matyas< S, M >

class	minitensor::McCormick< S, M >

class	minitensor::StyblinskiTang< S, M >

class	minitensor::Paraboloid< S, M >

class	minitensor::Rosenbrock< S, M >

class	minitensor::Beale< S, M >

class	minitensor::Booth< S, M >

class	minitensor::GoldsteinPrice< S, M >

class	minitensor::Failure< S, M >

class	minitensor::Mesa< S, M >

class	minitensor::Sigmoid< S, M >

class	minitensor::Identity< S, NC, NV >

class	minitensor::Nonlinear01< S, NC, NV >

class	minitensor::Circumference< S, NC, NV >

class	minitensor::Circle< S, NC, NV >

Typedefs
template<typename T , int N>
using	minitensor::FAD = Sacado::Fad::SLFad< T, N >
	The Fad type to use.

Enumerations
enum class	minitensor::StepType { minitensor::StepType::UNDEFINED = 0 , minitensor::StepType::NEWTON = 1 , minitensor::StepType::NEWTON_LS = 2 , minitensor::StepType::TRUST_REGION = 3 , minitensor::StepType::CG = 4 , minitensor::StepType::LINE_SEARCH_REG = 5 }

Functions
	minitensor::Function_Base< FunctionDerived, S, M >::Function_Base ()

template<typename T , Index N>
T	minitensor::Function_Base< FunctionDerived, S, M >::value (FunctionDerived &f, Vector< T, N > const &x)

template<typename T , Index N>
Vector< T, N >	minitensor::Function_Base< FunctionDerived, S, M >::gradient (FunctionDerived &f, Vector< T, N > const &x)

template<typename T , Index N>
Vector< T, N >	minitensor::Function_Base< FunctionDerived, S, M >::residual (FunctionDerived &f, Vector< T, N > const &x)

template<typename T , Index N>
Tensor< T, N >	minitensor::Function_Base< FunctionDerived, S, M >::hessian (FunctionDerived &f, Vector< T, N > const &x)

void	minitensor::Function_Base< FunctionDerived, S, M >::set_failed (char const *const msg=nullptr)

bool	minitensor::Function_Base< FunctionDerived, S, M >::get_failed ()

void	minitensor::Function_Base< FunctionDerived, S, M >::clear_failed ()

void	minitensor::Function_Base< FunctionDerived, S, M >::set_failure_message (char const *const msg=nullptr)

char const *	minitensor::Function_Base< FunctionDerived, S, M >::get_failure_message ()

	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::Equality_Constraint ()

template<typename T , Index N>
Vector< T, NC >	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::value (ConstraintDerived &c, Vector< T, N > const &x)

template<typename T , Index N>
Matrix< T, NC, NV >	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::gradient (ConstraintDerived &c, Vector< T, N > const &x)

	minitensor::Bounds< T, N >::Bounds (Vector< T, N > const &l, Vector< T, N > const &u)

	minitensor::Minimizer< T, N >::Minimizer ()

template<typename STEP , typename FN >
void	minitensor::Minimizer< T, N >::solve (STEP &step_method, FN &fn, Vector< T, N > &x)

void	minitensor::Minimizer< T, N >::printReport (std::ostream &os)

void	minitensor::Minimizer< T, N >::updateConvergenceCriterion (T const abs_error)

void	minitensor::Minimizer< T, N >::updateDivergenceCriterion (T const fn_value)

bool	minitensor::Minimizer< T, N >::continueSolve () const

template<typename FN >
void	minitensor::Minimizer< T, N >::recordFinals (FN &fn, Vector< T, N > const &x)

template<typename FN >
Vector< T, N >	minitensor::NewtonLineSearch< T, N >::step (FN &fn, Vector< T, N > const &direction, Vector< T, N > const &soln)

template<typename FN >
Vector< T, N >	minitensor::BacktrackingLineSearch< T, N >::step (FN &fn, Vector< T, N > const &direction, Vector< T, N > const &soln)

Vector< T, N >	minitensor::TrustRegionSubproblemBase< T, N >::lin_solve (Tensor< T, N > const &A, Vector< T, N > const &b)

Vector< T, N >	minitensor::TrustRegionExactValue< T, N >::step (Tensor< T, N > const &Hessian, Vector< T, N > const &gradient)

Vector< T, N >	minitensor::TrustRegionExactGradient< T, N >::step (Tensor< T, N > const &Hessian, Vector< T, N > const &gradient)

Vector< T, N >	minitensor::TrustRegionDogLegValue< T, N >::step (Tensor< T, N > const &Hessian, Vector< T, N > const &gradient)

Vector< T, N >	minitensor::TrustRegionDogLegGradient< T, N >::step (Tensor< T, N > const &Hessian, Vector< T, N > const &gradient)

	minitensor::StepBase< FN, T, N >::StepBase ()

virtual char const *	minitensor::StepBase< FN, T, N >::name ()=0

virtual void	minitensor::StepBase< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)=0

virtual Vector< T, N >	minitensor::StepBase< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)=0

virtual	minitensor::StepBase< FN, T, N >::~StepBase ()

Vector< T, N >	minitensor::StepBase< FN, T, N >::lin_solve (Tensor< T, N > const &A, Vector< T, N > const &b)

template<typename FN , typename T , Index N>
std::unique_ptr< StepBase< FN, T, N > >	minitensor::stepFactory (StepType step_type)

virtual char const *	minitensor::NewtonStep< FN, T, N >::name ()

virtual void	minitensor::NewtonStep< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual Vector< T, N >	minitensor::NewtonStep< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual	minitensor::NewtonStep< FN, T, N >::~NewtonStep ()

virtual char const *	minitensor::NewtonWithLineSearchStep< FN, T, N >::name ()

virtual void	minitensor::NewtonWithLineSearchStep< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual Vector< T, N >	minitensor::NewtonWithLineSearchStep< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual	minitensor::NewtonWithLineSearchStep< FN, T, N >::~NewtonWithLineSearchStep ()

virtual char const *	minitensor::TrustRegionStep< FN, T, N >::name ()

virtual void	minitensor::TrustRegionStep< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual Vector< T, N >	minitensor::TrustRegionStep< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual	minitensor::TrustRegionStep< FN, T, N >::~TrustRegionStep ()

virtual char const *	minitensor::ConjugateGradientStep< FN, T, N >::name ()

virtual void	minitensor::ConjugateGradientStep< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual Vector< T, N >	minitensor::ConjugateGradientStep< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual	minitensor::ConjugateGradientStep< FN, T, N >::~ConjugateGradientStep ()

virtual char const *	minitensor::LineSearchRegularizedStep< FN, T, N >::name ()

virtual void	minitensor::LineSearchRegularizedStep< FN, T, N >::initialize (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual Vector< T, N >	minitensor::LineSearchRegularizedStep< FN, T, N >::step (FN &fn, Vector< T, N > const &x, Vector< T, N > const &r)

virtual	minitensor::LineSearchRegularizedStep< FN, T, N >::~LineSearchRegularizedStep ()

Variables
static constexpr Index	minitensor::Function_Base< FunctionDerived, S, M >::DIMENSION {M}

bool	minitensor::Function_Base< FunctionDerived, S, M >::failed {false}

char const *	minitensor::Function_Base< FunctionDerived, S, M >::failure_message {nullptr}
	Keep a message to inform what went wrong above.

static constexpr bool	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::IS_EQUALITY {true}

bool	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::failed {false}

static constexpr Index	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::NUM_CONSTR {NC}

static constexpr Index	minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::NUM_VAR {NV}

static constexpr bool	minitensor::Inequality_Constraint< ConstraintDerived, S, NC, NV >::IS_EQUALITY {false}

Vector< T, N >	minitensor::Bounds< T, N >::lower

Vector< T, N >	minitensor::Bounds< T, N >::upper

Index	minitensor::Minimizer< T, N >::max_num_iter {256}

Index	minitensor::Minimizer< T, N >::min_num_iter {0}

Index	minitensor::Minimizer< T, N >::num_iter {0}

Index	minitensor::Minimizer< T, N >::num_stagnation_iter {0}

Index	minitensor::Minimizer< T, N >::max_stagnation_iter {0}

T	minitensor::Minimizer< T, N >::initial_norm {1.0}

T	minitensor::Minimizer< T, N >::rel_tol {1.0e-12}

T	minitensor::Minimizer< T, N >::rel_error {1.0}

T	minitensor::Minimizer< T, N >::abs_tol {1.0e-12}

T	minitensor::Minimizer< T, N >::acc_tol {1.0e-12}

T	minitensor::Minimizer< T, N >::stagnation_tol {1.0}

T	minitensor::Minimizer< T, N >::abs_error {1.0}

T	minitensor::Minimizer< T, N >::growth_limit {1.0}

T	minitensor::Minimizer< T, N >::initial_value {0.0}

T	minitensor::Minimizer< T, N >::previous_value {0.0}

T	minitensor::Minimizer< T, N >::final_value {0.0}

bool	minitensor::Minimizer< T, N >::failed {false}

bool	minitensor::Minimizer< T, N >::warning {false}

bool	minitensor::Minimizer< T, N >::converged {false}

bool	minitensor::Minimizer< T, N >::monotonic {true}

bool	minitensor::Minimizer< T, N >::bounded {true}

bool	minitensor::Minimizer< T, N >::non_stagnant {true}

bool	minitensor::Minimizer< T, N >::enforce_monotonicity {false}

bool	minitensor::Minimizer< T, N >::enforce_boundedness {false}

bool	minitensor::Minimizer< T, N >::enforce_non_stagnation {false}

Vector< T, N >	minitensor::Minimizer< T, N >::initial_guess

Vector< T, N >	minitensor::Minimizer< T, N >::final_soln

Vector< T, N >	minitensor::Minimizer< T, N >::final_gradient

Tensor< T, N >	minitensor::Minimizer< T, N >::final_hessian

char const *	minitensor::Minimizer< T, N >::step_method_name {nullptr}

char const *	minitensor::Minimizer< T, N >::function_name {nullptr}

char const *	minitensor::Minimizer< T, N >::failure_message {"No failure detected"}

char const *	minitensor::Minimizer< T, N >::warning_message {"No warning detected"}

Index	minitensor::NewtonLineSearch< T, N >::max_num_iter {16}

T	minitensor::NewtonLineSearch< T, N >::tolerance {1.0e-6}

Index	minitensor::BacktrackingLineSearch< T, N >::max_num_iter {100}

Index	minitensor::BacktrackingLineSearch< T, N >::max_line_iter {10}

T	minitensor::BacktrackingLineSearch< T, N >::search_parameter {0.5}

T	minitensor::BacktrackingLineSearch< T, N >::search_increment {0.1}

T	minitensor::BacktrackingLineSearch< T, N >::alpha {1.0}

T	minitensor::BacktrackingLineSearch< T, N >::tolerance {1.0e-6}

PreconditionerType	minitensor::TrustRegionSubproblemBase< T, N >::preconditioner_type {PreconditionerType::IDENTITY}

Index	minitensor::TrustRegionExactValue< T, N >::max_num_iter {4}

T	minitensor::TrustRegionExactValue< T, N >::region_size {1.0}

Index	minitensor::TrustRegionExactGradient< T, N >::max_num_iter {4}

T	minitensor::TrustRegionExactGradient< T, N >::region_size {1.0}

T	minitensor::TrustRegionDogLegValue< T, N >::region_size {1.0}

T	minitensor::TrustRegionDogLegGradient< T, N >::region_size {1.0}

PreconditionerType	minitensor::StepBase< FN, T, N >::preconditioner_type {PreconditionerType::IDENTITY}

static constexpr char const *const	minitensor::NewtonStep< FN, T, N >::NAME {"Newton"}

static constexpr char const *const	minitensor::NewtonWithLineSearchStep< FN, T, N >::NAME {"Newton with Line Search"}

static constexpr char const *const	minitensor::TrustRegionStep< FN, T, N >::NAME {"Trust Region"}

T	minitensor::TrustRegionStep< FN, T, N >::max_region_size {10.0}

T	minitensor::TrustRegionStep< FN, T, N >::initial_region_size {10.0}

T	minitensor::TrustRegionStep< FN, T, N >::min_reduction {0.0}

T	minitensor::TrustRegionStep< FN, T, N >::region_size {0.0}

static constexpr char const *const	minitensor::ConjugateGradientStep< FN, T, N >::NAME {"Preconditioned Conjugate Gradient"}

Index	minitensor::ConjugateGradientStep< FN, T, N >::restart_directions_interval {32}

Vector< T, N >	minitensor::ConjugateGradientStep< FN, T, N >::search_direction

Vector< T, N >	minitensor::ConjugateGradientStep< FN, T, N >::precon_resi

T	minitensor::ConjugateGradientStep< FN, T, N >::projection_new {0.0}

Index	minitensor::ConjugateGradientStep< FN, T, N >::restart_directions_counter {0}

static constexpr char const *const	minitensor::LineSearchRegularizedStep< FN, T, N >::NAME {"Line Search Regularized"}

T	minitensor::LineSearchRegularizedStep< FN, T, N >::step_length {1.0}

T	minitensor::LineSearchRegularizedStep< FN, T, N >::hessian_cond_tol {1.0e+08}

Detailed Description

Nonlinear system solvers, unconstrained and constrained optimization methods, and benchmark test functions.

Typedef Documentation

◆ FAD

template<typename T , int N>

using minitensor::FAD = typedef Sacado::Fad::SLFad<T, N>

The Fad type to use.

Definition at line 27 of file MiniTensor_Solvers.h.

Enumeration Type Documentation

◆ StepType

enum class minitensor::StepType

strong

The step types

Enumerator
UNDEFINED
NEWTON
NEWTON_LS
TRUST_REGION
CG
LINE_SEARCH_REG

Definition at line 728 of file MiniTensor_Solvers.h.

Function Documentation

◆ Function_Base()

template<typename FunctionDerived , typename S , Index M>

minitensor::Function_Base< FunctionDerived, S, M >::Function_Base ( )

inline

Definition at line 46 of file MiniTensor_Solvers.h.

◆ value() [1/2]

template<typename FunctionDerived , typename S , Index M>

template<typename T , Index N>

T minitensor::Function_Base< FunctionDerived, S, M >::value	(	FunctionDerived &	f,
		Vector< T, N > const &	x
	)

By default use merit function 0.5 dot(residual,residual) as the target to optimize if only the residual is provided.

Definition at line 1038 of file MiniTensor_Solvers.h.

◆ gradient() [1/2]

template<typename FunctionDerived , typename S , Index M>

template<typename T , Index N>

Vector< T, N > minitensor::Function_Base< FunctionDerived, S, M >::gradient	(	FunctionDerived &	f,
		Vector< T, N > const &	x
	)

By default compute gradient with AD from value().

Definition at line 1055 of file MiniTensor_Solvers.h.

◆ residual()

template<typename FunctionDerived , typename S , Index M>

template<typename T , Index N>

Vector< T, N > minitensor::Function_Base< FunctionDerived, S, M >::residual	(	FunctionDerived &	f,
		Vector< T, N > const &	x
	)

Defined explicitly.

Definition at line 1091 of file MiniTensor_Solvers.h.

◆ hessian()

template<typename FunctionDerived , typename S , Index M>

template<typename T , Index N>

Tensor< T, N > minitensor::Function_Base< FunctionDerived, S, M >::hessian	(	FunctionDerived &	f,
		Vector< T, N > const &	x
	)

By default compute Hessian with AD from gradient().

Definition at line 1103 of file MiniTensor_Solvers.h.

◆ set_failed()

template<typename FunctionDerived , typename S , Index M>

void minitensor::Function_Base< FunctionDerived, S, M >::set_failed ( char const *const msg = nullptr )

Mark the function as failed and optionally set a failure message.

Definition at line 1140 of file MiniTensor_Solvers.h.

◆ get_failed()

template<typename FunctionDerived , typename S , Index M>

bool minitensor::Function_Base< FunctionDerived, S, M >::get_failed ( )

Return whether the function has failed.

Definition at line 1153 of file MiniTensor_Solvers.h.

◆ clear_failed()

template<typename FunctionDerived , typename S , Index M>

void minitensor::Function_Base< FunctionDerived, S, M >::clear_failed ( )

Clear the failure flag.

Definition at line 1164 of file MiniTensor_Solvers.h.

◆ set_failure_message()

template<typename FunctionDerived , typename S , Index M>

void minitensor::Function_Base< FunctionDerived, S, M >::set_failure_message ( char const *const msg = nullptr )

Set the failure message.

Definition at line 1176 of file MiniTensor_Solvers.h.

◆ get_failure_message()

template<typename FunctionDerived , typename S , Index M>

char const * minitensor::Function_Base< FunctionDerived, S, M >::get_failure_message ( )

Return the failure message.

Definition at line 1188 of file MiniTensor_Solvers.h.

◆ Equality_Constraint()

template<typename ConstraintDerived , typename S , Index NC, Index NV>

minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::Equality_Constraint ( )

inline

Definition at line 130 of file MiniTensor_Solvers.h.

◆ value() [2/2]

template<typename ConstraintDerived , typename S , Index NC, Index NV>

template<typename T , Index N>

Vector< T, NC > minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::value	(	ConstraintDerived &	c,
		Vector< T, N > const &	x
	)

Return the value of the constraints at point x.

Definition at line 1200 of file MiniTensor_Solvers.h.

◆ gradient() [2/2]

template<typename ConstraintDerived , typename S , Index NC, Index NV>

template<typename T , Index N>

Matrix< T, NC, NV > minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::gradient	(	ConstraintDerived &	c,
		Vector< T, N > const &	x
	)

By default compute gradient with AD from value().

Definition at line 1213 of file MiniTensor_Solvers.h.

◆ Bounds()

template<typename T , Index N>

minitensor::Bounds< T, N >::Bounds	(	Vector< T, N > const &	l,
		Vector< T, N > const &	u
	)

Construct bounds from lower bound l and upper bound u.

Definition at line 1252 of file MiniTensor_Solvers.h.

◆ Minimizer()

template<typename T , Index N>

minitensor::Minimizer< T, N >::Minimizer ( )

Definition at line 1262 of file MiniTensor_Solvers.h.

◆ solve()

template<typename T , Index N>

template<typename STEP , typename FN >

void minitensor::Minimizer< T, N >::solve	(	STEP &	step_method,
		FN &	fn,
		Vector< T, N > &	x
	)

Minimize the function fn starting from x using the given step method. On return x contains the solution found.

Definition at line 1279 of file MiniTensor_Solvers.h.

◆ printReport()

template<typename T , Index N>

void minitensor::Minimizer< T, N >::printReport ( std::ostream & os )

Print a summary report of the minimization to the stream os.

Definition at line 1336 of file MiniTensor_Solvers.h.

◆ updateConvergenceCriterion()

template<typename T , Index N>

void minitensor::Minimizer< T, N >::updateConvergenceCriterion ( T const abs_error )

private

Update the absolute and relative errors and the convergence status.

Definition at line 1376 of file MiniTensor_Solvers.h.

◆ updateDivergenceCriterion()

template<typename T , Index N>

void minitensor::Minimizer< T, N >::updateDivergenceCriterion ( T const fn_value )

private

Update the monotonicity, stagnation and boundedness status with the latest function value.

Definition at line 1407 of file MiniTensor_Solvers.h.

◆ continueSolve()

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::continueSolve ( ) const

private

Return whether the iteration loop should continue.

Definition at line 1451 of file MiniTensor_Solvers.h.

◆ recordFinals()

template<typename T , Index N>

template<typename FN >

void minitensor::Minimizer< T, N >::recordFinals	(	FN &	fn,
		Vector< T, N > const &	x
	)

private

Record the final solution, function value, gradient and Hessian.

Definition at line 1490 of file MiniTensor_Solvers.h.

◆ step() [1/12]

template<typename T , Index N>

template<typename FN >

Vector< T, N > minitensor::NewtonLineSearch< T, N >::step	(	FN &	fn,
		Vector< T, N > const &	direction,
		Vector< T, N > const &	soln
	)

Perform a Newton line search from soln along direction and return the resulting step.

Definition at line 1755 of file MiniTensor_Solvers.h.

◆ step() [2/12]

template<typename T , Index N>

template<typename FN >

Vector< T, N > minitensor::BacktrackingLineSearch< T, N >::step	(	FN &	fn,
		Vector< T, N > const &	direction,
		Vector< T, N > const &	soln
	)

Perform a back-tracking line search from soln along direction and return the resulting step.

Definition at line 1809 of file MiniTensor_Solvers.h.

◆ lin_solve() [1/2]

template<typename T , Index N>

Vector< T, N > minitensor::TrustRegionSubproblemBase< T, N >::lin_solve	(	Tensor< T, N > const &	A,
		Vector< T, N > const &	b
	)

Solve the linear system \( A x = b \) with preconditioning.

Definition at line 1515 of file MiniTensor_Solvers.h.

◆ step() [3/12]

template<typename T , Index N>

Vector< T, N > minitensor::TrustRegionExactValue< T, N >::step	(	Tensor< T, N > const &	Hessian,
		Vector< T, N > const &	gradient
	)

Compute the trust-region step for the given Hessian and gradient.

Definition at line 1527 of file MiniTensor_Solvers.h.

◆ step() [4/12]

template<typename T , Index N>

Vector< T, N > minitensor::TrustRegionExactGradient< T, N >::step	(	Tensor< T, N > const &	Hessian,
		Vector< T, N > const &	gradient
	)

Compute the trust-region step for the given Hessian and gradient.

Definition at line 1591 of file MiniTensor_Solvers.h.

◆ step() [5/12]

template<typename T , Index N>

Vector< T, N > minitensor::TrustRegionDogLegValue< T, N >::step	(	Tensor< T, N > const &	Hessian,
		Vector< T, N > const &	gradient
	)

Compute the dog-leg step for the given Hessian and gradient.

Definition at line 1662 of file MiniTensor_Solvers.h.

◆ step() [6/12]

template<typename T , Index N>

Vector< T, N > minitensor::TrustRegionDogLegGradient< T, N >::step	(	Tensor< T, N > const &	Hessian,
		Vector< T, N > const &	gradient
	)

Compute the dog-leg step for the given Hessian and gradient.

Definition at line 1706 of file MiniTensor_Solvers.h.

◆ StepBase()

template<typename FN , typename T , Index N>

minitensor::StepBase< FN, T, N >::StepBase ( )

inline

Definition at line 677 of file MiniTensor_Solvers.h.

◆ name() [1/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::StepBase< FN, T, N >::name ( )

pure virtual

Return the name of the step method.

Implemented in minitensor::NewtonStep< FN, T, N >, minitensor::NewtonWithLineSearchStep< FN, T, N >, minitensor::TrustRegionStep< FN, T, N >, minitensor::ConjugateGradientStep< FN, T, N >, and minitensor::LineSearchRegularizedStep< FN, T, N >.

◆ initialize() [1/6]

template<typename FN , typename T , Index N>

virtual void minitensor::StepBase< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

pure virtual

Initialize the step method with function fn, initial guess x and residual r.

Implemented in minitensor::NewtonStep< FN, T, N >, minitensor::NewtonWithLineSearchStep< FN, T, N >, minitensor::TrustRegionStep< FN, T, N >, minitensor::ConjugateGradientStep< FN, T, N >, and minitensor::LineSearchRegularizedStep< FN, T, N >.

◆ step() [7/12]

template<typename FN , typename T , Index N>

virtual Vector< T, N > minitensor::StepBase< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

pure virtual

Compute a step for function fn at point x with residual r.

Implemented in minitensor::NewtonStep< FN, T, N >, minitensor::NewtonWithLineSearchStep< FN, T, N >, minitensor::TrustRegionStep< FN, T, N >, minitensor::ConjugateGradientStep< FN, T, N >, and minitensor::LineSearchRegularizedStep< FN, T, N >.

◆ ~StepBase()

template<typename FN , typename T , Index N>

virtual minitensor::StepBase< FN, T, N >::~StepBase ( )

inlinevirtual

Definition at line 709 of file MiniTensor_Solvers.h.

◆ lin_solve() [2/2]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::StepBase< FN, T, N >::lin_solve	(	Tensor< T, N > const &	A,
		Vector< T, N > const &	b
	)

Solve the linear system \( A x = b \) with preconditioning.

Definition at line 1504 of file MiniTensor_Solvers.h.

◆ stepFactory()

template<typename FN , typename T , Index N>

std::unique_ptr< StepBase< FN, T, N > > minitensor::stepFactory ( StepType step_type )

Construct the step object for the given step type.

Definition at line 2194 of file MiniTensor_Solvers.h.

◆ name() [2/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::NewtonStep< FN, T, N >::name ( )

inlinevirtual

Return the name of the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 763 of file MiniTensor_Solvers.h.

◆ initialize() [2/6]

template<typename FN , typename T , Index N>

void minitensor::NewtonStep< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Initialize the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1894 of file MiniTensor_Solvers.h.

◆ step() [8/12]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::NewtonStep< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Compute a full Newton step.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1905 of file MiniTensor_Solvers.h.

◆ ~NewtonStep()

template<typename FN , typename T , Index N>

virtual minitensor::NewtonStep< FN, T, N >::~NewtonStep ( )

inlinevirtual

Definition at line 783 of file MiniTensor_Solvers.h.

◆ name() [3/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::NewtonWithLineSearchStep< FN, T, N >::name ( )

inlinevirtual

Return the name of the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 805 of file MiniTensor_Solvers.h.

◆ initialize() [3/6]

template<typename FN , typename T , Index N>

void minitensor::NewtonWithLineSearchStep< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Initialize the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1923 of file MiniTensor_Solvers.h.

◆ step() [9/12]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::NewtonWithLineSearchStep< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Compute a Newton step followed by a back-tracking line search.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1934 of file MiniTensor_Solvers.h.

◆ ~NewtonWithLineSearchStep()

template<typename FN , typename T , Index N>

virtual minitensor::NewtonWithLineSearchStep< FN, T, N >::~NewtonWithLineSearchStep ( )

inlinevirtual

Definition at line 826 of file MiniTensor_Solvers.h.

◆ name() [4/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::TrustRegionStep< FN, T, N >::name ( )

inlinevirtual

Return the name of the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 847 of file MiniTensor_Solvers.h.

◆ initialize() [4/6]

template<typename FN , typename T , Index N>

void minitensor::TrustRegionStep< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Initialize the trust-region radius.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1958 of file MiniTensor_Solvers.h.

◆ step() [10/12]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::TrustRegionStep< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Compute a trust-region step. See Nocedal 2nd Ed, algorithm 11.5.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 1971 of file MiniTensor_Solvers.h.

◆ ~TrustRegionStep()

template<typename FN , typename T , Index N>

virtual minitensor::TrustRegionStep< FN, T, N >::~TrustRegionStep ( )

inlinevirtual

Definition at line 868 of file MiniTensor_Solvers.h.

◆ name() [5/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::ConjugateGradientStep< FN, T, N >::name ( )

inlinevirtual

Return the name of the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 914 of file MiniTensor_Solvers.h.

◆ initialize() [5/6]

template<typename FN , typename T , Index N>

void minitensor::ConjugateGradientStep< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Initialize the search direction and preconditioned residual.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 2046 of file MiniTensor_Solvers.h.

◆ step() [11/12]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::ConjugateGradientStep< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Compute a preconditioned conjugate gradient step (Polak-Ribiere).

Implements minitensor::StepBase< FN, T, N >.

Definition at line 2072 of file MiniTensor_Solvers.h.

◆ ~ConjugateGradientStep()

template<typename FN , typename T , Index N>

virtual minitensor::ConjugateGradientStep< FN, T, N >::~ConjugateGradientStep ( )

inlinevirtual

Definition at line 936 of file MiniTensor_Solvers.h.

◆ name() [6/6]

template<typename FN , typename T , Index N>

virtual char const * minitensor::LineSearchRegularizedStep< FN, T, N >::name ( )

inlinevirtual

Return the name of the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 990 of file MiniTensor_Solvers.h.

◆ initialize() [6/6]

template<typename FN , typename T , Index N>

void minitensor::LineSearchRegularizedStep< FN, T, N >::initialize	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Initialize the step method.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 2134 of file MiniTensor_Solvers.h.

◆ step() [12/12]

template<typename FN , typename T , Index N>

Vector< T, N > minitensor::LineSearchRegularizedStep< FN, T, N >::step	(	FN &	fn,
		Vector< T, N > const &	x,
		Vector< T, N > const &	r
	)

virtual

Compute a regularized Newton step followed by a Newton line search. See Nocedal 2nd Ed, algorithm 11.4.

Implements minitensor::StepBase< FN, T, N >.

Definition at line 2145 of file MiniTensor_Solvers.h.

◆ ~LineSearchRegularizedStep()

template<typename FN , typename T , Index N>

virtual minitensor::LineSearchRegularizedStep< FN, T, N >::~LineSearchRegularizedStep ( )

inlinevirtual

Definition at line 1011 of file MiniTensor_Solvers.h.

Variable Documentation

◆ DIMENSION

template<typename FunctionDerived , typename S , Index M>

constexpr Index minitensor::Function_Base< FunctionDerived, S, M >::DIMENSION {M}

staticconstexpr

Maximum dimension of the argument vectors.

Definition at line 44 of file MiniTensor_Solvers.h.

◆ failed [1/3]

template<typename FunctionDerived , typename S , Index M>

bool minitensor::Function_Base< FunctionDerived, S, M >::failed {false}

protected

Signal that something has gone horribly wrong.

Definition at line 115 of file MiniTensor_Solvers.h.

◆ failure_message [1/2]

template<typename FunctionDerived , typename S , Index M>

char const* minitensor::Function_Base< FunctionDerived, S, M >::failure_message {nullptr}

protected

Keep a message to inform what went wrong above.

Definition at line 120 of file MiniTensor_Solvers.h.

◆ IS_EQUALITY [1/2]

template<typename ConstraintDerived , typename S , Index NC, Index NV>

constexpr bool minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::IS_EQUALITY {true}

staticconstexpr

This is an equality constraint.

Definition at line 153 of file MiniTensor_Solvers.h.

◆ failed [2/3]

template<typename ConstraintDerived , typename S , Index NC, Index NV>

bool minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::failed {false}

Signal that something has gone horribly wrong.

Definition at line 159 of file MiniTensor_Solvers.h.

◆ NUM_CONSTR

template<typename ConstraintDerived , typename S , Index NC, Index NV>

constexpr Index minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::NUM_CONSTR {NC}

staticconstexpr

Number of constraints.

Definition at line 166 of file MiniTensor_Solvers.h.

◆ NUM_VAR

template<typename ConstraintDerived , typename S , Index NC, Index NV>

constexpr Index minitensor::Equality_Constraint< ConstraintDerived, S, NC, NV >::NUM_VAR {NV}

staticconstexpr

Number of variables.

Definition at line 173 of file MiniTensor_Solvers.h.

◆ IS_EQUALITY [2/2]

template<typename ConstraintDerived , typename S , Index NC, Index NV>

constexpr bool minitensor::Inequality_Constraint< ConstraintDerived, S, NC, NV >::IS_EQUALITY {false}

staticconstexpr

This is not an equality constraint.

Definition at line 188 of file MiniTensor_Solvers.h.

◆ lower

template<typename T , Index N>

Vector<T, N> minitensor::Bounds< T, N >::lower

Lower bound.

Definition at line 206 of file MiniTensor_Solvers.h.

◆ upper

template<typename T , Index N>

Vector<T, N> minitensor::Bounds< T, N >::upper

Upper bound.

Definition at line 212 of file MiniTensor_Solvers.h.

◆ max_num_iter [1/5]

template<typename T , Index N>

Index minitensor::Minimizer< T, N >::max_num_iter {256}

Maximum number of iterations allowed.

Definition at line 273 of file MiniTensor_Solvers.h.

◆ min_num_iter

template<typename T , Index N>

Index minitensor::Minimizer< T, N >::min_num_iter {0}

Minimum number of iterations to perform.

Definition at line 279 of file MiniTensor_Solvers.h.

◆ num_iter

template<typename T , Index N>

Index minitensor::Minimizer< T, N >::num_iter {0}

Number of iterations taken.

Definition at line 285 of file MiniTensor_Solvers.h.

◆ num_stagnation_iter

template<typename T , Index N>

Index minitensor::Minimizer< T, N >::num_stagnation_iter {0}

Number of consecutive stagnant iterations so far.

Definition at line 291 of file MiniTensor_Solvers.h.

◆ max_stagnation_iter

template<typename T , Index N>

Index minitensor::Minimizer< T, N >::max_stagnation_iter {0}

Maximum number of consecutive stagnant iterations allowed.

Definition at line 298 of file MiniTensor_Solvers.h.

◆ initial_norm

template<typename T , Index N>

T minitensor::Minimizer< T, N >::initial_norm {1.0}

Norm of the initial residual, \( \|R_0\| \).

Definition at line 304 of file MiniTensor_Solvers.h.

◆ rel_tol

template<typename T , Index N>

T minitensor::Minimizer< T, N >::rel_tol {1.0e-12}

Relative error tolerance.

Definition at line 310 of file MiniTensor_Solvers.h.

◆ rel_error

template<typename T , Index N>

T minitensor::Minimizer< T, N >::rel_error {1.0}

Current relative error, \( \|R\| / \|R_0\| \).

Definition at line 316 of file MiniTensor_Solvers.h.

◆ abs_tol

template<typename T , Index N>

T minitensor::Minimizer< T, N >::abs_tol {1.0e-12}

Absolute error tolerance.

Definition at line 322 of file MiniTensor_Solvers.h.

◆ acc_tol

template<typename T , Index N>

T minitensor::Minimizer< T, N >::acc_tol {1.0e-12}

Acceptable absolute tolerance applied at the last iteration.

Definition at line 329 of file MiniTensor_Solvers.h.

◆ stagnation_tol

template<typename T , Index N>

T minitensor::Minimizer< T, N >::stagnation_tol {1.0}

Reduction ratio above which an iteration is considered stagnant.

Definition at line 336 of file MiniTensor_Solvers.h.

◆ abs_error

template<typename T , Index N>

T minitensor::Minimizer< T, N >::abs_error {1.0}

Current absolute error, \( \|R\| \).

Definition at line 342 of file MiniTensor_Solvers.h.

◆ growth_limit

template<typename T , Index N>

T minitensor::Minimizer< T, N >::growth_limit {1.0}

Growth factor over the initial value beyond which the objective function is considered unbounded.

Definition at line 349 of file MiniTensor_Solvers.h.

◆ initial_value

template<typename T , Index N>

T minitensor::Minimizer< T, N >::initial_value {0.0}

Initial value of the objective function.

Definition at line 355 of file MiniTensor_Solvers.h.

◆ previous_value

template<typename T , Index N>

T minitensor::Minimizer< T, N >::previous_value {0.0}

Value of the objective function at the previous iteration.

Definition at line 362 of file MiniTensor_Solvers.h.

◆ final_value

template<typename T , Index N>

T minitensor::Minimizer< T, N >::final_value {0.0}

Final value of the objective function.

Definition at line 368 of file MiniTensor_Solvers.h.

◆ failed [3/3]

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::failed {false}

Whether the minimization failed.

Definition at line 374 of file MiniTensor_Solvers.h.

◆ warning

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::warning {false}

Whether a warning was issued.

Definition at line 380 of file MiniTensor_Solvers.h.

◆ converged

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::converged {false}

Whether the minimization converged.

Definition at line 386 of file MiniTensor_Solvers.h.

◆ monotonic

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::monotonic {true}

Whether the objective function decreased monotonically.

Definition at line 392 of file MiniTensor_Solvers.h.

◆ bounded

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::bounded {true}

Whether the objective function remained bounded.

Definition at line 398 of file MiniTensor_Solvers.h.

◆ non_stagnant

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::non_stagnant {true}

Whether the iteration remained non-stagnant.

Definition at line 404 of file MiniTensor_Solvers.h.

◆ enforce_monotonicity

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::enforce_monotonicity {false}

If true, fail when the objective function is non-monotonic.

Definition at line 411 of file MiniTensor_Solvers.h.

◆ enforce_boundedness

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::enforce_boundedness {false}

If true, fail when the objective function grows unbounded.

Definition at line 418 of file MiniTensor_Solvers.h.

◆ enforce_non_stagnation

template<typename T , Index N>

bool minitensor::Minimizer< T, N >::enforce_non_stagnation {false}

If true, warn when the residual stagnates.

Definition at line 424 of file MiniTensor_Solvers.h.

◆ initial_guess

template<typename T , Index N>

Vector<T, N> minitensor::Minimizer< T, N >::initial_guess

Initial guess.

Definition at line 430 of file MiniTensor_Solvers.h.

◆ final_soln

template<typename T , Index N>

Vector<T, N> minitensor::Minimizer< T, N >::final_soln

Final solution.

Definition at line 436 of file MiniTensor_Solvers.h.

◆ final_gradient

template<typename T , Index N>

Vector<T, N> minitensor::Minimizer< T, N >::final_gradient

Gradient at the final solution.

Definition at line 442 of file MiniTensor_Solvers.h.

◆ final_hessian

template<typename T , Index N>

Tensor<T, N> minitensor::Minimizer< T, N >::final_hessian

Hessian at the final solution.

Definition at line 448 of file MiniTensor_Solvers.h.

◆ step_method_name

template<typename T , Index N>

char const* minitensor::Minimizer< T, N >::step_method_name {nullptr}

Name of the step method used.

Definition at line 454 of file MiniTensor_Solvers.h.

◆ function_name

template<typename T , Index N>

char const* minitensor::Minimizer< T, N >::function_name {nullptr}

Name of the function being minimized.

Definition at line 460 of file MiniTensor_Solvers.h.

◆ failure_message [2/2]

template<typename T , Index N>

char const* minitensor::Minimizer< T, N >::failure_message {"No failure detected"}

Message describing a failure, if any.

Definition at line 466 of file MiniTensor_Solvers.h.

◆ warning_message

template<typename T , Index N>

char const* minitensor::Minimizer< T, N >::warning_message {"No warning detected"}

Message describing a warning, if any.

Definition at line 472 of file MiniTensor_Solvers.h.

◆ max_num_iter [2/5]

template<typename T , Index N>

Index minitensor::NewtonLineSearch< T, N >::max_num_iter {16}

Maximum number of line search iterations.

Definition at line 493 of file MiniTensor_Solvers.h.

◆ tolerance [1/2]

template<typename T , Index N>

T minitensor::NewtonLineSearch< T, N >::tolerance {1.0e-6}

Convergence tolerance on the step length.

Definition at line 499 of file MiniTensor_Solvers.h.

◆ max_num_iter [3/5]

template<typename T , Index N>

Index minitensor::BacktrackingLineSearch< T, N >::max_num_iter {100}

Maximum number of iterations.

Definition at line 520 of file MiniTensor_Solvers.h.

◆ max_line_iter

template<typename T , Index N>

Index minitensor::BacktrackingLineSearch< T, N >::max_line_iter {10}

Maximum number of line iterations before increasing the search parameter.

Definition at line 527 of file MiniTensor_Solvers.h.

◆ search_parameter

template<typename T , Index N>

T minitensor::BacktrackingLineSearch< T, N >::search_parameter {0.5}

Sufficient-decrease parameter for the residual norm.

Definition at line 533 of file MiniTensor_Solvers.h.

◆ search_increment

template<typename T , Index N>

T minitensor::BacktrackingLineSearch< T, N >::search_increment {0.1}

Increment applied to the search parameter when the line iterations are exhausted.

Definition at line 540 of file MiniTensor_Solvers.h.

◆ alpha

template<typename T , Index N>

T minitensor::BacktrackingLineSearch< T, N >::alpha {1.0}

Line search step length multiplier.

Definition at line 546 of file MiniTensor_Solvers.h.

◆ tolerance [2/2]

template<typename T , Index N>

T minitensor::BacktrackingLineSearch< T, N >::tolerance {1.0e-6}

Convergence tolerance.

Definition at line 552 of file MiniTensor_Solvers.h.

◆ preconditioner_type [1/2]

template<typename T , Index N>

PreconditionerType minitensor::TrustRegionSubproblemBase< T, N >::preconditioner_type {PreconditionerType::IDENTITY}

Preconditioner used by the linear solver.

Definition at line 565 of file MiniTensor_Solvers.h.

◆ max_num_iter [4/5]

template<typename T , Index N>

Index minitensor::TrustRegionExactValue< T, N >::max_num_iter {4}

Maximum number of iterations for the subproblem.

Definition at line 593 of file MiniTensor_Solvers.h.

◆ region_size [1/5]

template<typename T , Index N>

T minitensor::TrustRegionExactValue< T, N >::region_size {1.0}

Trust-region radius \( \Delta \).

Definition at line 599 of file MiniTensor_Solvers.h.

◆ max_num_iter [5/5]

template<typename T , Index N>

Index minitensor::TrustRegionExactGradient< T, N >::max_num_iter {4}

Maximum number of iterations for the subproblem.

Definition at line 620 of file MiniTensor_Solvers.h.

◆ region_size [2/5]

template<typename T , Index N>

T minitensor::TrustRegionExactGradient< T, N >::region_size {1.0}

Trust-region radius \( \Delta \).

Definition at line 626 of file MiniTensor_Solvers.h.

◆ region_size [3/5]

template<typename T , Index N>

T minitensor::TrustRegionDogLegValue< T, N >::region_size {1.0}

Trust-region radius \( \Delta \).

Definition at line 647 of file MiniTensor_Solvers.h.

◆ region_size [4/5]

template<typename T , Index N>

T minitensor::TrustRegionDogLegGradient< T, N >::region_size {1.0}

Trust-region radius \( \Delta \).

Definition at line 668 of file MiniTensor_Solvers.h.

◆ preconditioner_type [2/2]

template<typename FN , typename T , Index N>

PreconditionerType minitensor::StepBase< FN, T, N >::preconditioner_type {PreconditionerType::IDENTITY}

Preconditioner used by the linear solver.

Definition at line 715 of file MiniTensor_Solvers.h.

◆ NAME [1/5]

template<typename FN , typename T , Index N>

constexpr char const* const minitensor::NewtonStep< FN, T, N >::NAME {"Newton"}

staticconstexpr

Name of the step method.

Definition at line 756 of file MiniTensor_Solvers.h.

◆ NAME [2/5]

template<typename FN , typename T , Index N>

constexpr char const* const minitensor::NewtonWithLineSearchStep< FN, T, N >::NAME {"Newton with Line Search"}

staticconstexpr

Name of the step method.

Definition at line 798 of file MiniTensor_Solvers.h.

◆ NAME [3/5]

template<typename FN , typename T , Index N>

constexpr char const* const minitensor::TrustRegionStep< FN, T, N >::NAME {"Trust Region"}

staticconstexpr

Name of the step method.

Definition at line 840 of file MiniTensor_Solvers.h.

◆ max_region_size

template<typename FN , typename T , Index N>

T minitensor::TrustRegionStep< FN, T, N >::max_region_size {10.0}

Maximum trust-region radius.

Definition at line 874 of file MiniTensor_Solvers.h.

◆ initial_region_size

template<typename FN , typename T , Index N>

T minitensor::TrustRegionStep< FN, T, N >::initial_region_size {10.0}

Initial trust-region radius.

Definition at line 880 of file MiniTensor_Solvers.h.

◆ min_reduction

template<typename FN , typename T , Index N>

T minitensor::TrustRegionStep< FN, T, N >::min_reduction {0.0}

Minimum reduction ratio to accept a step.

Definition at line 886 of file MiniTensor_Solvers.h.

◆ region_size [5/5]

template<typename FN , typename T , Index N>

T minitensor::TrustRegionStep< FN, T, N >::region_size {0.0}

private

Current trust-region radius \( \Delta \).

Definition at line 893 of file MiniTensor_Solvers.h.

◆ NAME [4/5]

template<typename FN , typename T , Index N>

constexpr char const* const minitensor::ConjugateGradientStep< FN, T, N >::NAME {"Preconditioned Conjugate Gradient"}

staticconstexpr

Name of the step method.

Definition at line 907 of file MiniTensor_Solvers.h.

◆ restart_directions_interval

template<typename FN , typename T , Index N>

Index minitensor::ConjugateGradientStep< FN, T, N >::restart_directions_interval {32}

Number of iterations between restarts of the search directions.

Definition at line 943 of file MiniTensor_Solvers.h.

◆ search_direction

template<typename FN , typename T , Index N>

Vector<T, N> minitensor::ConjugateGradientStep< FN, T, N >::search_direction

private

Current search direction.

Definition at line 950 of file MiniTensor_Solvers.h.

◆ precon_resi

template<typename FN , typename T , Index N>

Vector<T, N> minitensor::ConjugateGradientStep< FN, T, N >::precon_resi

private

Preconditioned residual.

Definition at line 956 of file MiniTensor_Solvers.h.

◆ projection_new

template<typename FN , typename T , Index N>

T minitensor::ConjugateGradientStep< FN, T, N >::projection_new {0.0}

private

Latest projection used by the Polak-Ribiere formula.

Definition at line 962 of file MiniTensor_Solvers.h.

◆ restart_directions_counter

template<typename FN , typename T , Index N>

Index minitensor::ConjugateGradientStep< FN, T, N >::restart_directions_counter {0}

private

Iterations since the last restart of the search directions.

Definition at line 969 of file MiniTensor_Solvers.h.

◆ NAME [5/5]

template<typename FN , typename T , Index N>

constexpr char const* const minitensor::LineSearchRegularizedStep< FN, T, N >::NAME {"Line Search Regularized"}

staticconstexpr

Name of the step method.

Definition at line 983 of file MiniTensor_Solvers.h.

◆ step_length

template<typename FN , typename T , Index N>

T minitensor::LineSearchRegularizedStep< FN, T, N >::step_length {1.0}

Trust-region size used to regularize a bad Hessian.

Definition at line 1017 of file MiniTensor_Solvers.h.

◆ hessian_cond_tol

template<typename FN , typename T , Index N>

T minitensor::LineSearchRegularizedStep< FN, T, N >::hessian_cond_tol {1.0e+08}

Hessian condition number above which regularization is applied.

Definition at line 1024 of file MiniTensor_Solvers.h.

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ FAD

Enumeration Type Documentation

◆ StepType

Function Documentation

◆ Function_Base()

◆ value() [1/2]

◆ gradient() [1/2]

◆ residual()

◆ hessian()

◆ set_failed()

◆ get_failed()

◆ clear_failed()

◆ set_failure_message()

◆ get_failure_message()

◆ Equality_Constraint()

◆ value() [2/2]

◆ gradient() [2/2]

◆ Bounds()

◆ Minimizer()

◆ solve()

◆ printReport()

◆ updateConvergenceCriterion()

◆ updateDivergenceCriterion()

◆ continueSolve()

◆ recordFinals()

◆ step() [1/12]

◆ step() [2/12]

◆ lin_solve() [1/2]

◆ step() [3/12]

◆ step() [4/12]

◆ step() [5/12]

◆ step() [6/12]

◆ StepBase()

◆ name() [1/6]

◆ initialize() [1/6]

◆ step() [7/12]

◆ ~StepBase()

◆ lin_solve() [2/2]

◆ stepFactory()

◆ name() [2/6]

◆ initialize() [2/6]

◆ step() [8/12]

◆ ~NewtonStep()

◆ name() [3/6]

◆ initialize() [3/6]

◆ step() [9/12]

◆ ~NewtonWithLineSearchStep()

◆ name() [4/6]

◆ initialize() [4/6]

◆ step() [10/12]

◆ ~TrustRegionStep()

◆ name() [5/6]

◆ initialize() [5/6]

◆ step() [11/12]

◆ ~ConjugateGradientStep()

◆ name() [6/6]

◆ initialize() [6/6]

◆ step() [12/12]

◆ ~LineSearchRegularizedStep()

Variable Documentation

◆ DIMENSION

◆ failed [1/3]

◆ failure_message [1/2]

◆ IS_EQUALITY [1/2]

◆ failed [2/3]

◆ NUM_CONSTR

◆ NUM_VAR

◆ IS_EQUALITY [2/2]

◆ lower

◆ upper

◆ max_num_iter [1/5]

◆ min_num_iter

◆ num_iter