#include <alpaqa/problem/type-erased-problem.hpp>

Detailed Description

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>
class alpaqa::TypeErasedProblem< Conf, Allocator >

The main polymorphic minimization problem interface.

This class wraps the actual problem implementation class, filling in the missing member functions with sensible defaults, and providing a uniform interface that is used by the solvers.

The problem implementations do not inherit from an abstract base class. Instead, structural typing is used. The ProblemVTable constructor uses reflection to discover which member functions are provided by the problem implementation. See Problem formulations for more information, and C++/CustomCppProblem/main.cpp for an example.

Definition at line 237 of file type-erased-problem.hpp.

Inheritance diagram for TypeErasedProblem< Conf, Allocator >:

Collaboration diagram for TypeErasedProblem< Conf, Allocator >:

Problem dimensions
length_t	get_num_variables () const
	[Required] Number of decision variables.
length_t	get_num_constraints () const
	[Required] Number of constraints.

Required cost and constraint functions
real_t	eval_objective (crvec x) const
	[Required] Function that evaluates the cost, \( f(x) \)
void	eval_objective_gradient (crvec x, rvec grad_fx) const
	[Required] Function that evaluates the gradient of the cost, \( \nabla f(x) \)
void	eval_constraints (crvec x, rvec gx) const
	[Required] Function that evaluates the constraints, \( g(x) \)
void	eval_constraints_gradient_product (crvec x, crvec y, rvec grad_gxy) const
	[Required] Function that evaluates the gradient of the constraints times a vector, \( \nabla g(x)\,y = \tp{\jac_g(x)}y \)

Projections onto constraint sets and proximal mappings
void	eval_projecting_difference_constraints (crvec z, rvec e) const
	[Required] Function that evaluates the difference between the given point \( z \) and its projection onto the constraint set \( D \).
void	eval_projection_multipliers (rvec y, real_t M) const
	[Required] Function that projects the Lagrange multipliers for ALM.
real_t	eval_proximal_gradient_step (real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p) const
	[Required] Function that computes a proximal gradient step.
index_t	eval_inactive_indices_res_lna (real_t γ, crvec x, crvec grad_ψ, rindexvec J) const
	[Optional] Function that computes the inactive indices \( \mathcal J(x) \) for the evaluation of the linear Newton approximation of the residual, as in [4].

Constraint sets
const Box &	get_variable_bounds () const
	[Optional] Get the rectangular constraint set of the decision variables, \( x \in C \).
const Box &	get_general_bounds () const
	[Optional] Get the rectangular constraint set of the general constraint function, \( g(x) \in D \).

Functions for second-order solvers
void	eval_constraints_jacobian (crvec x, rvec J_values) const
	[Optional] Function that evaluates the nonzero values of the Jacobian matrix of the constraints, \( \jac_g(x) \)
Sparsity	get_constraints_jacobian_sparsity () const
	[Optional] Function that returns (a view of) the sparsity pattern of the Jacobian of the constraints.
void	eval_grad_gi (crvec x, index_t i, rvec grad_gi) const
	[Optional] Function that evaluates the gradient of one specific constraint, \( \nabla g_i(x) \)
void	eval_lagrangian_hessian_product (crvec x, crvec y, real_t scale, crvec v, rvec Hv) const
	[Optional] Function that evaluates the Hessian of the Lagrangian multiplied by a vector, \( \nabla_{xx}^2L(x, y)\,v \)
void	eval_lagrangian_hessian (crvec x, crvec y, real_t scale, rvec H_values) const
	[Optional] Function that evaluates the nonzero values of the Hessian of the Lagrangian, \( \nabla_{xx}^2L(x, y) \)
Sparsity	get_lagrangian_hessian_sparsity () const
	[Optional] Function that returns (a view of) the sparsity pattern of the Hessian of the Lagrangian.
void	eval_augmented_lagrangian_hessian_product (crvec x, crvec y, crvec Σ, real_t scale, crvec v, rvec Hv) const
	[Optional] Function that evaluates the Hessian of the augmented Lagrangian multiplied by a vector, \( \nabla_{xx}^2L_\Sigma(x, y)\,v \)
void	eval_augmented_lagrangian_hessian (crvec x, crvec y, crvec Σ, real_t scale, rvec H_values) const
	[Optional] Function that evaluates the nonzero values of the Hessian of the augmented Lagrangian, \( \nabla_{xx}^2L_\Sigma(x, y) \)
Sparsity	get_augmented_lagrangian_hessian_sparsity () const
	[Optional] Function that returns (a view of) the sparsity pattern of the Hessian of the augmented Lagrangian.

Combined evaluations
real_t	eval_objective_and_gradient (crvec x, rvec grad_fx) const
	[Optional] Evaluate both \( f(x) \) and its gradient, \( \nabla f(x) \).
real_t	eval_objective_and_constraints (crvec x, rvec g) const
	[Optional] Evaluate both \( f(x) \) and \( g(x) \).
void	eval_objective_gradient_and_constraints_gradient_product (crvec x, crvec y, rvec grad_f, rvec grad_gxy) const
	[Optional] Evaluate both \( \nabla f(x) \) and \( \nabla g(x)\,y \).
void	eval_lagrangian_gradient (crvec x, crvec y, rvec grad_L, rvec work_n) const
	[Optional] Evaluate the gradient of the Lagrangian \( \nabla_x L(x, y) = \nabla f(x) + \nabla g(x)\,y \)

Augmented Lagrangian
real_t	eval_augmented_lagrangian (crvec x, crvec y, crvec Σ, rvec ŷ) const
	[Optional] Calculate both ψ(x) and the vector ŷ that can later be used to compute ∇ψ.
void	eval_augmented_lagrangian_gradient (crvec x, crvec y, crvec Σ, rvec grad_ψ, rvec work_n, rvec work_m) const
	[Optional] Calculate the gradient ∇ψ(x).
real_t	eval_augmented_lagrangian_and_gradient (crvec x, crvec y, crvec Σ, rvec grad_ψ, rvec work_n, rvec work_m) const
	[Optional] Calculate both ψ(x) and its gradient ∇ψ(x).

Checks
void	check () const
	[Optional] Check that the problem formulation is well-defined, the dimensions match, etc.

Metadata
std::string	get_name () const
	[Optional] Get a descriptive name for the problem.

Querying specialized implementations
bool	provides_eval_inactive_indices_res_lna () const
	Returns true if the problem provides an implementation of eval_inactive_indices_res_lna.
bool	provides_eval_constraints_jacobian () const
	Returns true if the problem provides an implementation of eval_constraints_jacobian.
bool	provides_get_constraints_jacobian_sparsity () const
	Returns true if the problem provides an implementation of get_constraints_jacobian_sparsity.
bool	provides_eval_grad_gi () const
	Returns true if the problem provides an implementation of eval_grad_gi.
bool	provides_eval_lagrangian_hessian_product () const
	Returns true if the problem provides an implementation of eval_lagrangian_hessian_product.
bool	provides_eval_lagrangian_hessian () const
	Returns true if the problem provides an implementation of eval_lagrangian_hessian.
bool	provides_get_lagrangian_hessian_sparsity () const
	Returns true if the problem provides an implementation of get_lagrangian_hessian_sparsity.
bool	provides_eval_augmented_lagrangian_hessian_product () const
	Returns true if the problem provides an implementation of eval_augmented_lagrangian_hessian_product.
bool	provides_eval_augmented_lagrangian_hessian () const
	Returns true if the problem provides an implementation of eval_augmented_lagrangian_hessian.
bool	provides_get_augmented_lagrangian_hessian_sparsity () const
	Returns true if the problem provides an implementation of get_augmented_lagrangian_hessian_sparsity.
bool	provides_eval_objective_and_gradient () const
	Returns true if the problem provides a specialized implementation of eval_objective_and_gradient, false if it uses the default implementation.
bool	provides_eval_objective_and_constraints () const
	Returns true if the problem provides a specialized implementation of eval_objective_and_constraints, false if it uses the default implementation.
bool	provides_eval_objective_gradient_and_constraints_gradient_product () const
	Returns true if the problem provides a specialized implementation of eval_objective_gradient_and_constraints_gradient_product, false if it uses the default implementation.
bool	provides_eval_lagrangian_gradient () const
	Returns true if the problem provides a specialized implementation of eval_lagrangian_gradient, false if it uses the default implementation.
bool	provides_eval_augmented_lagrangian () const
	Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian, false if it uses the default implementation.
bool	provides_eval_augmented_lagrangian_gradient () const
	Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian_gradient, false if it uses the default implementation.
bool	provides_eval_augmented_lagrangian_and_gradient () const
	Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian_and_gradient, false if it uses the default implementation.
bool	provides_get_variable_bounds () const
	Returns true if the problem provides an implementation of get_variable_bounds.
bool	provides_get_general_bounds () const
	Returns true if the problem provides an implementation of get_general_bounds.
bool	provides_check () const
	Returns true if the problem provides an implementation of check.
bool	provides_get_name () const
	Returns true if the problem provides an implementation of get_name.

Querying available functions
bool	supports_eval_augmented_lagrangian_hessian_product () const
	Returns true if eval_augmented_lagrangian_hessian_product can be called.
bool	supports_eval_augmented_lagrangian_hessian () const
	Returns true if eval_augmented_lagrangian_hessian can be called.

Helpers
real_t	calc_ŷ_dᵀŷ (rvec g_ŷ, crvec y, crvec Σ) const
	Given g(x), compute the intermediate results ŷ and dᵀŷ that can later be used to compute ψ(x) and ∇ψ(x).

Public Types
using	Box = alpaqa::Box<config_t>
using	VTable = ProblemVTable<config_t>
using	allocator_type = Allocator
using	TypeErased = guanaqo::TypeErased<VTable, allocator_type>

Static Public Member Functions
template<class T, class... Args>
static TypeErasedProblem	make (Args &&...args)

Member Typedef Documentation

◆ Box

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

using Box = alpaqa::Box<config_t>

Definition at line 240 of file type-erased-problem.hpp.

◆ VTable

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

using VTable = ProblemVTable<config_t>

Definition at line 241 of file type-erased-problem.hpp.

◆ allocator_type

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

using allocator_type = Allocator

Definition at line 242 of file type-erased-problem.hpp.

◆ TypeErased

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

using TypeErased = guanaqo::TypeErased<VTable, allocator_type>

Definition at line 243 of file type-erased-problem.hpp.

Member Function Documentation

◆ make()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

template<class T, class... Args>

TypeErasedProblem make ( Args &&... args )

inlinestatic

Definition at line 253 of file type-erased-problem.hpp.

◆ get_num_variables()

template<Config Conf, class Allocator>

auto get_num_variables ( ) const

nodiscard

[Required] Number of decision variables.

Definition at line 763 of file type-erased-problem.hpp.

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◆ get_num_constraints()

template<Config Conf, class Allocator>

auto get_num_constraints ( ) const

nodiscard

[Required] Number of constraints.

Definition at line 767 of file type-erased-problem.hpp.

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◆ eval_objective()

template<Config Conf, class Allocator>

auto eval_objective ( crvec x ) const

nodiscard

[Required] Function that evaluates the cost, \( f(x) \)

Parameters

[in] x Decision variable \( x \in \R^n \)

Definition at line 792 of file type-erased-problem.hpp.

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◆ eval_objective_gradient()

template<Config Conf, class Allocator>

void eval_objective_gradient	(	crvec	x,
		rvec	grad_fx ) const

[Required] Function that evaluates the gradient of the cost, \( \nabla f(x) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[out]	grad_fx	Gradient of cost function \( \nabla f(x) \in \R^n \)

Definition at line 796 of file type-erased-problem.hpp.

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◆ eval_constraints()

template<Config Conf, class Allocator>

void eval_constraints	(	crvec	x,
		rvec	gx ) const

[Required] Function that evaluates the constraints, \( g(x) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[out]	gx	Value of the constraints \( g(x) \in \R^m \)

Definition at line 800 of file type-erased-problem.hpp.

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◆ eval_constraints_gradient_product()

template<Config Conf, class Allocator>

void eval_constraints_gradient_product	(	crvec	x,
		crvec	y,
		rvec	grad_gxy ) const

[Required] Function that evaluates the gradient of the constraints times a vector, \( \nabla g(x)\,y = \tp{\jac_g(x)}y \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	y	Vector \( y \in \R^m \) to multiply the gradient by
[out]	grad_gxy	Gradient of the constraints \( \nabla g(x)\,y \in \R^n \)

Definition at line 804 of file type-erased-problem.hpp.

◆ eval_projecting_difference_constraints()

template<Config Conf, class Allocator>

void eval_projecting_difference_constraints	(	crvec	z,
		rvec	e ) const

[Required] Function that evaluates the difference between the given point \( z \) and its projection onto the constraint set \( D \).

Parameters

[in]	z	Slack variable, \( z \in \R^m \)
[out]	e	The difference relative to its projection, \( e = z - \Pi_D(z) \in \R^m \)

Note: z and e can refer to the same vector.

Definition at line 772 of file type-erased-problem.hpp.

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◆ eval_projection_multipliers()

template<Config Conf, class Allocator>

void eval_projection_multipliers	(	rvec	y,
		real_t	M ) const

[Required] Function that projects the Lagrange multipliers for ALM.

Parameters

[in,out]	y	Multipliers, \( y \leftarrow \Pi_Y(y) \in \R^m \)
[in]	M	The radius/size of the set \( Y \). See max_multiplier.

Definition at line 777 of file type-erased-problem.hpp.

◆ eval_proximal_gradient_step()

template<Config Conf, class Allocator>

auto eval_proximal_gradient_step	(	real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rvec	x̂,
		rvec	p ) const

[Required] Function that computes a proximal gradient step.

Parameters

[in]	γ	Step size, \( \gamma \in \R_{>0} \)
[in]	x	Decision variable \( x \in \R^n \)
[in]	grad_ψ	Gradient of the subproblem cost, \( \nabla\psi(x) \in \R^n \)
[out]	x̂	Next proximal gradient iterate, \( \hat x = T_\gamma(x) = \prox_{\gamma h}(x - \gamma\nabla\psi(x)) \in \R^n \)
[out]	p	The proximal gradient step, \( p = \hat x - x \in \R^n \)

Returns: The nonsmooth function evaluated at x̂, \( h(\hat x) \).

Note: The vector \( p \) is often used in stopping criteria, so its numerical accuracy is more important than that of \( \hat x \).

Definition at line 781 of file type-erased-problem.hpp.

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◆ eval_inactive_indices_res_lna()

template<Config Conf, class Allocator>

auto eval_inactive_indices_res_lna	(	real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rindexvec	J ) const

nodiscard

[Optional] Function that computes the inactive indices \( \mathcal J(x) \) for the evaluation of the linear Newton approximation of the residual, as in [4].

Parameters

[in]	γ	Step size, \( \gamma \in \R_{>0} \)
[in]	x	Decision variable \( x \in \R^n \)
[in]	grad_ψ	Gradient of the subproblem cost, \( \nabla\psi(x) \in \R^n \)
[out]	J	The indices of the components of \( x \) that are in the index set \( \mathcal J(x) \). In ascending order, at most n.

Returns: The number of inactive constraints, \( \# \mathcal J(x) \).

For example, in the case of box constraints, we have

\[ \mathcal J(x) \defeq \defset{i \in \N_{[0, n-1]}}{\underline x_i \lt x_i - \gamma\nabla_{\!x_i}\psi(x) \lt \overline x_i}. \]

Definition at line 787 of file type-erased-problem.hpp.

◆ get_variable_bounds()

template<Config Conf, class Allocator>

auto get_variable_bounds ( ) const

nodiscard

[Optional] Get the rectangular constraint set of the decision variables, \( x \in C \).

Definition at line 894 of file type-erased-problem.hpp.

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◆ get_general_bounds()

template<Config Conf, class Allocator>

auto get_general_bounds ( ) const

nodiscard

[Optional] Get the rectangular constraint set of the general constraint function, \( g(x) \in D \).

Definition at line 898 of file type-erased-problem.hpp.

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◆ eval_constraints_jacobian()

template<Config Conf, class Allocator>

void eval_constraints_jacobian	(	crvec	x,
		rvec	J_values ) const

[Optional] Function that evaluates the nonzero values of the Jacobian matrix of the constraints, \( \jac_g(x) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[out]	J_values	Nonzero values of the Jacobian \( \jac_g(x) \in \R^{m\times n} \)

Required for second-order solvers only.

Definition at line 813 of file type-erased-problem.hpp.

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◆ get_constraints_jacobian_sparsity()

template<Config Conf, class Allocator>

auto get_constraints_jacobian_sparsity ( ) const

nodiscard

[Optional] Function that returns (a view of) the sparsity pattern of the Jacobian of the constraints.

Required for second-order solvers only.

Definition at line 817 of file type-erased-problem.hpp.

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◆ eval_grad_gi()

template<Config Conf, class Allocator>

void eval_grad_gi	(	crvec	x,
		index_t	i,
		rvec	grad_gi ) const

[Optional] Function that evaluates the gradient of one specific constraint, \( \nabla g_i(x) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	i	Which constraint \( 0 \le i \lt m \)
[out]	grad_gi	Gradient of the constraint \( \nabla g_i(x) \in \R^n \)

Required for second-order solvers only.

Definition at line 809 of file type-erased-problem.hpp.

◆ eval_lagrangian_hessian_product()

template<Config Conf, class Allocator>

void eval_lagrangian_hessian_product	(	crvec	x,
		crvec	y,
		real_t	scale,
		crvec	v,
		rvec	Hv ) const

[Optional] Function that evaluates the Hessian of the Lagrangian multiplied by a vector, \( \nabla_{xx}^2L(x, y)\,v \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	y	Lagrange multipliers \( y \in \R^m \)
[in]	scale	Scale factor for the cost function.
[in]	v	Vector to multiply by \( v \in \R^n \)
[out]	Hv	Hessian-vector product \( \nabla_{xx}^2 L(x, y)\,v \in \R^{n} \)

Required for second-order solvers only.

Definition at line 821 of file type-erased-problem.hpp.

◆ eval_lagrangian_hessian()

template<Config Conf, class Allocator>

void eval_lagrangian_hessian	(	crvec	x,
		crvec	y,
		real_t	scale,
		rvec	H_values ) const

[Optional] Function that evaluates the nonzero values of the Hessian of the Lagrangian, \( \nabla_{xx}^2L(x, y) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	y	Lagrange multipliers \( y \in \R^m \)
[in]	scale	Scale factor for the cost function.
[out]	H_values	Nonzero values of the Hessian \( \nabla_{xx}^2 L(x, y) \in \R^{n\times n} \).

Required for second-order solvers only.

Definition at line 827 of file type-erased-problem.hpp.

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◆ get_lagrangian_hessian_sparsity()

template<Config Conf, class Allocator>

auto get_lagrangian_hessian_sparsity ( ) const

nodiscard

[Optional] Function that returns (a view of) the sparsity pattern of the Hessian of the Lagrangian.

Required for second-order solvers only.

Definition at line 832 of file type-erased-problem.hpp.

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◆ eval_augmented_lagrangian_hessian_product()

template<Config Conf, class Allocator>

void eval_augmented_lagrangian_hessian_product	(	crvec	x,
		crvec	y,
		crvec	Σ,
		real_t	scale,
		crvec	v,
		rvec	Hv ) const

[Optional] Function that evaluates the Hessian of the augmented Lagrangian multiplied by a vector, \( \nabla_{xx}^2L_\Sigma(x, y)\,v \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	y	Lagrange multipliers \( y \in \R^m \)
[in]	Σ	Penalty weights \( \Sigma \)
[in]	scale	Scale factor for the cost function.
[in]	v	Vector to multiply by \( v \in \R^n \)
[out]	Hv	Hessian-vector product \( \nabla_{xx}^2 L_\Sigma(x, y)\,v \in \R^{n} \)

Required for second-order solvers only.

Definition at line 836 of file type-erased-problem.hpp.

◆ eval_augmented_lagrangian_hessian()

template<Config Conf, class Allocator>

void eval_augmented_lagrangian_hessian	(	crvec	x,
		crvec	y,
		crvec	Σ,
		real_t	scale,
		rvec	H_values ) const

[Optional] Function that evaluates the nonzero values of the Hessian of the augmented Lagrangian, \( \nabla_{xx}^2L_\Sigma(x, y) \)

Parameters

[in]	x	Decision variable \( x \in \R^n \)
[in]	y	Lagrange multipliers \( y \in \R^m \)
[in]	Σ	Penalty weights \( \Sigma \)
[in]	scale	Scale factor for the cost function.
[out]	H_values	Nonzero values of the Hessian \( \nabla_{xx}^2 L_\Sigma(x, y) \in \R^{n\times n} \)

Required for second-order solvers only.

Definition at line 841 of file type-erased-problem.hpp.

◆ get_augmented_lagrangian_hessian_sparsity()

template<Config Conf, class Allocator>

auto get_augmented_lagrangian_hessian_sparsity ( ) const

nodiscard

[Optional] Function that returns (a view of) the sparsity pattern of the Hessian of the augmented Lagrangian.

Required for second-order solvers only.

Definition at line 847 of file type-erased-problem.hpp.

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◆ eval_objective_and_gradient()

template<Config Conf, class Allocator>

auto eval_objective_and_gradient	(	crvec	x,
		rvec	grad_fx ) const

[Optional] Evaluate both \( f(x) \) and its gradient, \( \nabla f(x) \).

Default implementation:: ProblemVTable::default_eval_objective_and_gradient

Definition at line 852 of file type-erased-problem.hpp.

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◆ eval_objective_and_constraints()

template<Config Conf, class Allocator>

auto eval_objective_and_constraints	(	crvec	x,
		rvec	g ) const

[Optional] Evaluate both \( f(x) \) and \( g(x) \).

Default implementation:: ProblemVTable::default_eval_objective_and_constraints

Definition at line 857 of file type-erased-problem.hpp.

◆ eval_objective_gradient_and_constraints_gradient_product()

template<Config Conf, class Allocator>

void eval_objective_gradient_and_constraints_gradient_product	(	crvec	x,
		crvec	y,
		rvec	grad_f,
		rvec	grad_gxy ) const

[Optional] Evaluate both \( \nabla f(x) \) and \( \nabla g(x)\,y \).

Default implementation:: ProblemVTable::default_eval_objective_gradient_and_constraints_gradient_product

Definition at line 862 of file type-erased-problem.hpp.

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◆ eval_lagrangian_gradient()

template<Config Conf, class Allocator>

void eval_lagrangian_gradient	(	crvec	x,
		crvec	y,
		rvec	grad_L,
		rvec	work_n ) const

[Optional] Evaluate the gradient of the Lagrangian \( \nabla_x L(x, y) = \nabla f(x) + \nabla g(x)\,y \)

Default implementation:: ProblemVTable::default_eval_lagrangian_gradient

Definition at line 868 of file type-erased-problem.hpp.

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◆ eval_augmented_lagrangian()

template<Config Conf, class Allocator>

auto eval_augmented_lagrangian	(	crvec	x,
		crvec	y,
		crvec	Σ,
		rvec	ŷ ) const

nodiscard

[Optional] Calculate both ψ(x) and the vector ŷ that can later be used to compute ∇ψ.

\[ \psi(x) = f(x) + \tfrac{1}{2} \text{dist}_\Sigma^2\left(g(x) + \Sigma^{-1}y,\;D\right) \]

\[ \hat y = \Sigma\, \left(g(x) + \Sigma^{-1}y - \Pi_D\left(g(x) + \Sigma^{-1}y\right)\right) \]

Default implementation:: ProblemVTable::default_eval_augmented_lagrangian

Parameters

[in]	x	Decision variable \( x \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[out]	ŷ	\( \hat y \)

Definition at line 873 of file type-erased-problem.hpp.

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◆ eval_augmented_lagrangian_gradient()

template<Config Conf, class Allocator>

void eval_augmented_lagrangian_gradient	(	crvec	x,
		crvec	y,
		crvec	Σ,
		rvec	grad_ψ,
		rvec	work_n,
		rvec	work_m ) const

[Optional] Calculate the gradient ∇ψ(x).

\[ \nabla \psi(x) = \nabla f(x) + \nabla g(x)\,\hat y(x) \]

Default implementation:: ProblemVTable::default_eval_augmented_lagrangian_gradient

Parameters

[in]	x	Decision variable \( x \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[out]	grad_ψ	\( \nabla \psi(x) \)
	work_n	Dimension \( n \)
	work_m	Dimension \( m \)

Definition at line 878 of file type-erased-problem.hpp.

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◆ eval_augmented_lagrangian_and_gradient()

template<Config Conf, class Allocator>

auto eval_augmented_lagrangian_and_gradient	(	crvec	x,
		crvec	y,
		crvec	Σ,
		rvec	grad_ψ,
		rvec	work_n,
		rvec	work_m ) const

nodiscard

[Optional] Calculate both ψ(x) and its gradient ∇ψ(x).

\[ \psi(x) = f(x) + \tfrac{1}{2} \text{dist}_\Sigma^2\left(g(x) + \Sigma^{-1}y,\;D\right) \]

\[ \nabla \psi(x) = \nabla f(x) + \nabla g(x)\,\hat y(x) \]

Default implementation:: ProblemVTable::default_eval_augmented_lagrangian_and_gradient

Parameters

[in]	x	Decision variable \( x \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[out]	grad_ψ	\( \nabla \psi(x) \)
	work_n	Dimension \( n \)
	work_m	Dimension \( m \)

Definition at line 885 of file type-erased-problem.hpp.

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◆ check()

template<Config Conf, class Allocator>

void check ( ) const

[Optional] Check that the problem formulation is well-defined, the dimensions match, etc.

Throws an exception if this is not the case.

Definition at line 902 of file type-erased-problem.hpp.

◆ get_name()

template<Config Conf, class Allocator>

std::string get_name ( ) const

nodiscard

[Optional] Get a descriptive name for the problem.

Definition at line 906 of file type-erased-problem.hpp.

◆ provides_eval_inactive_indices_res_lna()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_inactive_indices_res_lna ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_inactive_indices_res_lna.

Definition at line 595 of file type-erased-problem.hpp.

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◆ provides_eval_constraints_jacobian()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_constraints_jacobian ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_constraints_jacobian.

Definition at line 600 of file type-erased-problem.hpp.

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◆ provides_get_constraints_jacobian_sparsity()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_constraints_jacobian_sparsity ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_constraints_jacobian_sparsity.

Definition at line 605 of file type-erased-problem.hpp.

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◆ provides_eval_grad_gi()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_grad_gi ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_grad_gi.

Definition at line 611 of file type-erased-problem.hpp.

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◆ provides_eval_lagrangian_hessian_product()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_lagrangian_hessian_product ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_lagrangian_hessian_product.

Definition at line 616 of file type-erased-problem.hpp.

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◆ provides_eval_lagrangian_hessian()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_lagrangian_hessian ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_lagrangian_hessian.

Definition at line 622 of file type-erased-problem.hpp.

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◆ provides_get_lagrangian_hessian_sparsity()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_lagrangian_hessian_sparsity ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_lagrangian_hessian_sparsity.

Definition at line 627 of file type-erased-problem.hpp.

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◆ provides_eval_augmented_lagrangian_hessian_product()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_augmented_lagrangian_hessian_product ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_augmented_lagrangian_hessian_product.

Definition at line 633 of file type-erased-problem.hpp.

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◆ provides_eval_augmented_lagrangian_hessian()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_augmented_lagrangian_hessian ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of eval_augmented_lagrangian_hessian.

Definition at line 639 of file type-erased-problem.hpp.

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◆ provides_get_augmented_lagrangian_hessian_sparsity()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_augmented_lagrangian_hessian_sparsity ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_augmented_lagrangian_hessian_sparsity.

Definition at line 645 of file type-erased-problem.hpp.

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◆ provides_eval_objective_and_gradient()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_objective_and_gradient ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_objective_and_gradient, false if it uses the default implementation.

Definition at line 651 of file type-erased-problem.hpp.

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◆ provides_eval_objective_and_constraints()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_objective_and_constraints ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_objective_and_constraints, false if it uses the default implementation.

Definition at line 656 of file type-erased-problem.hpp.

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◆ provides_eval_objective_gradient_and_constraints_gradient_product()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_objective_gradient_and_constraints_gradient_product ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_objective_gradient_and_constraints_gradient_product, false if it uses the default implementation.

Definition at line 662 of file type-erased-problem.hpp.

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◆ provides_eval_lagrangian_gradient()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_lagrangian_gradient ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_lagrangian_gradient, false if it uses the default implementation.

Definition at line 668 of file type-erased-problem.hpp.

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◆ provides_eval_augmented_lagrangian()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_augmented_lagrangian ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian, false if it uses the default implementation.

Definition at line 673 of file type-erased-problem.hpp.

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◆ provides_eval_augmented_lagrangian_gradient()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_augmented_lagrangian_gradient ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian_gradient, false if it uses the default implementation.

Definition at line 678 of file type-erased-problem.hpp.

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◆ provides_eval_augmented_lagrangian_and_gradient()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_eval_augmented_lagrangian_and_gradient ( ) const

inlinenodiscard

Returns true if the problem provides a specialized implementation of eval_augmented_lagrangian_and_gradient, false if it uses the default implementation.

Definition at line 684 of file type-erased-problem.hpp.

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◆ provides_get_variable_bounds()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_variable_bounds ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_variable_bounds.

Definition at line 690 of file type-erased-problem.hpp.

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◆ provides_get_general_bounds()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_general_bounds ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_general_bounds.

Definition at line 695 of file type-erased-problem.hpp.

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◆ provides_check()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_check ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of check.

Definition at line 699 of file type-erased-problem.hpp.

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◆ provides_get_name()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool provides_get_name ( ) const

inlinenodiscard

Returns true if the problem provides an implementation of get_name.

Definition at line 701 of file type-erased-problem.hpp.

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◆ supports_eval_augmented_lagrangian_hessian_product()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool supports_eval_augmented_lagrangian_hessian_product ( ) const

inlinenodiscard

Returns true if eval_augmented_lagrangian_hessian_product can be called.

Definition at line 711 of file type-erased-problem.hpp.

◆ supports_eval_augmented_lagrangian_hessian()

template<Config Conf = DefaultConfig, class Allocator = std::allocator<std::byte>>

bool supports_eval_augmented_lagrangian_hessian ( ) const

inlinenodiscard

Returns true if eval_augmented_lagrangian_hessian can be called.

Definition at line 716 of file type-erased-problem.hpp.

◆ calc_ŷ_dᵀŷ()

template<Config Conf, class Allocator>

auto calc_ŷ_dᵀŷ	(	rvec	g_ŷ,
		crvec	y,
		crvec	Σ ) const

Given g(x), compute the intermediate results ŷ and dᵀŷ that can later be used to compute ψ(x) and ∇ψ(x).

Computes the result using the following algorithm:

\[ \begin{aligned} \zeta &= g(x) + \Sigma^{-1} y \\[] d &= \zeta - \Pi_D(\zeta) = \operatorname{eval\_proj\_diff\_g}(\zeta, \zeta) \\[] \hat y &= \Sigma d \\[] \end{aligned} \]

See also: page_math

Parameters

[in,out]	g_ŷ	Input \( g(x) \), outputs \( \hat y \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)

Returns: The inner product \( d^\top \hat y \)

Definition at line 890 of file type-erased-problem.hpp.

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

src/alpaqa/include/alpaqa/problem/type-erased-problem.hpp

Detailed Description

Problem dimensions

Required cost and constraint functions

Projections onto constraint sets and proximal mappings

Constraint sets

Functions for second-order solvers

Combined evaluations

Augmented Lagrangian

Checks

Metadata

Querying specialized implementations

Querying available functions

Helpers

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ Box

◆ VTable

◆ allocator_type

◆ TypeErased

Member Function Documentation

◆ make()

◆ get_num_variables()

◆ get_num_constraints()

◆ eval_objective()

◆ eval_objective_gradient()

◆ eval_constraints()

◆ eval_constraints_gradient_product()

◆ eval_projecting_difference_constraints()

◆ eval_projection_multipliers()

◆ eval_proximal_gradient_step()

◆ eval_inactive_indices_res_lna()

◆ get_variable_bounds()

◆ get_general_bounds()

◆ eval_constraints_jacobian()

◆ get_constraints_jacobian_sparsity()

◆ eval_grad_gi()

◆ eval_lagrangian_hessian_product()

◆ eval_lagrangian_hessian()

◆ get_lagrangian_hessian_sparsity()

◆ eval_augmented_lagrangian_hessian_product()

◆ eval_augmented_lagrangian_hessian()

◆ get_augmented_lagrangian_hessian_sparsity()

◆ eval_objective_and_gradient()

◆ eval_objective_and_constraints()

◆ eval_objective_gradient_and_constraints_gradient_product()

◆ eval_lagrangian_gradient()

◆ eval_augmented_lagrangian()

◆ eval_augmented_lagrangian_gradient()

◆ eval_augmented_lagrangian_and_gradient()

◆ check()

◆ get_name()

◆ provides_eval_inactive_indices_res_lna()

◆ provides_eval_constraints_jacobian()

◆ provides_get_constraints_jacobian_sparsity()

◆ provides_eval_grad_gi()

◆ provides_eval_lagrangian_hessian_product()

◆ provides_eval_lagrangian_hessian()

◆ provides_get_lagrangian_hessian_sparsity()

◆ provides_eval_augmented_lagrangian_hessian_product()

◆ provides_eval_augmented_lagrangian_hessian()

◆ provides_get_augmented_lagrangian_hessian_sparsity()

◆ provides_eval_objective_and_gradient()

◆ provides_eval_objective_and_constraints()

◆ provides_eval_objective_gradient_and_constraints_gradient_product()

◆ provides_eval_lagrangian_gradient()

◆ provides_eval_augmented_lagrangian()

◆ provides_eval_augmented_lagrangian_gradient()

◆ provides_eval_augmented_lagrangian_and_gradient()

◆ provides_get_variable_bounds()

◆ provides_get_general_bounds()

◆ provides_check()

◆ provides_get_name()

◆ supports_eval_augmented_lagrangian_hessian_product()

◆ supports_eval_augmented_lagrangian_hessian()

◆ calc_ŷ_dᵀŷ()