Generic implementation of box constrained quasi-Newton algorithms. More...

#include <BoxConstrainedAlgorithm.hpp>

Static Public Member Functions
static bool	check_bounds (Problem &problem)
	Verify that the bounds are correct. More...

static Vector< Scalar >	truncate_x (Problem &problem, const Vector< Scalar > &x)
	Truncate vector such that it fulfills the box constraints. More...

static Scalar	gradient_norm (Problem &problem, const Vector< Scalar > &x, const Vector< Scalar > &g)
	Calculate the projected gradient norm ( $L_\infty$ norm) More...

static Scalar	max_step_length (Problem &problem, const Vector< Scalar > &x, const Vector< Scalar > &p)
	Calculate the maximum allowed step length. More...

template<typename OutputFunction >
static Vector< Scalar >	search_direction (Problem &problem, Storage &storage, const Vector< Scalar > &x, const Vector< Scalar > &g, const Scalar &check_epsilon, const Scalar &machine_epsilon, OutputFunction &output_function)
	Calculate the new search direction. More...

Detailed Description

template<typename Problem, typename Scalar, typename Storage>
struct LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >

Generic implementation of box constrained quasi-Newton algorithms.

Template Parameters

Problem	The optimization problem type.
Scalar	The scalar type of vector/matrix coefficients.
Storage	The algorithm storage, i.e. BFGS, L-BFGS etc.

Member Function Documentation

◆ check_bounds()

template<typename Problem , typename Scalar , typename Storage >

bool LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >::check_bounds ( Problem & problem )

static

Verify that the bounds are correct.

Parameters

problem The minimization problem (including box constraints).

Returns: true if the bounds are ok, false otherwise

◆ gradient_norm()

template<typename Problem , typename Scalar , typename Storage >

Scalar LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >::gradient_norm	(	Problem &	problem,
		const Vector< Scalar > &	x,
		const Vector< Scalar > &	g
	)

static

Calculate the projected gradient norm ( $L_\infty$ norm)

Parameters

problem	The minimization problem (including box constraints).
x	Current $\mathbf{x}$ value.
g	Current gradient for gradient norm calculation.

Returns: The projected gradient norm ( $L_\infty$ norm).

◆ max_step_length()

template<typename Problem , typename Scalar , typename Storage >

Scalar LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >::max_step_length	(	Problem &	problem,
		const Vector< Scalar > &	x,
		const Vector< Scalar > &	p
	)

static

Calculate the maximum allowed step length.

Parameters

problem	The minimization problem (including box constraints).
x	Current $\mathbf{x}$ value.
p	Current search direction.

Returns: Maximum allowed step length that does not violate the bounds.

◆ search_direction()

template<typename Problem , typename Scalar , typename Storage >

template<typename OutputFunction >

Vector< Scalar > LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >::search_direction	(	Problem &	problem,
		Storage &	storage,
		const Vector< Scalar > &	x,
		const Vector< Scalar > &	g,
		const Scalar &	check_epsilon,
		const Scalar &	machine_epsilon,
		OutputFunction &	output_function
	)

static

Calculate the new search direction.

Parameters

problem	The minimization problem (including box constraints).
storage	The storage for calculation of Hessian vector products.
x	Current $\mathbf{x}$ value.
g	Current gradient.
check_epsilon	Small value to check numerical stability.
machine_epsilon	Small value with machine accuracy.
output_function	Function for status output.

This function first calculates the generalized cauchy point and then performs a direct primal subspace minimization.

This technique is described in:

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization. 1995. SIAM Journal of Scientific and Statistical Computing. 16(5). 1190-1208.

Todo:: It must be checked if this is something that just happens or if this points to some subtle bug.

◆ truncate_x()

template<typename Problem , typename Scalar , typename Storage >

Vector< Scalar > LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >::truncate_x	(	Problem &	problem,
		const Vector< Scalar > &	x
	)

static

Truncate vector such that it fulfills the box constraints.

Parameters

problem	The minimization problem (including box constraints).
x	Vector to truncate.

Returns: The truncated x vector.

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

include/LSLOpt/Implementation/BoxConstrainedAlgorithm.hpp

Static Public Member Functions

Detailed Description

template<typename Problem, typename Scalar, typename Storage> struct LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >

Member Function Documentation

◆ check_bounds()

◆ gradient_norm()

◆ max_step_length()

◆ search_direction()

◆ truncate_x()

template<typename Problem, typename Scalar, typename Storage>
struct LSLOpt::Implementation::BoxConstrainedAlgorithm< Problem, Scalar, Storage >