#include <alpaqa/problem/box-constr-problem.hpp>

Detailed Description

template<Config Conf>
class alpaqa::BoxConstrProblem< Conf >

Implements common problem functions for minimization problems with box constraints.

Meant to be used as a base class for custom problem implementations. Supports optional \( \ell_1 \)-regularization.

Examples: C++/CustomCppProblem/main.cpp, and C++/FortranProblem/main.cpp.

Definition at line 16 of file box-constr-problem.hpp.

Inheritance diagram for BoxConstrProblem< Conf >:

Collaboration diagram for BoxConstrProblem< Conf >:

Public Types
using	Box = alpaqa::Box< config_t >

Public Member Functions
	BoxConstrProblem (length_t n, length_t m)
	Create a problem with inactive boxes \( (-\infty, +\infty) \), with no \( \ell_1 \)-regularization, and all general constraints handled using ALM.

	BoxConstrProblem (Box C, Box D, vec l1_reg=vec(0), index_t penalty_alm_split=0)

void	resize (length_t n, length_t m)
	Change the dimensions of the problem (number of decision variables and number of constaints).

	BoxConstrProblem (const BoxConstrProblem &)=default

BoxConstrProblem &	operator= (const BoxConstrProblem &)=default

	BoxConstrProblem (BoxConstrProblem &&) noexcept=default

BoxConstrProblem &	operator= (BoxConstrProblem &&) noexcept=default

length_t	get_n () const
	Number of decision variables, n.

length_t	get_m () const
	Number of constraints, m.

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

void	eval_proj_diff_g (crvec z, rvec p) const

void	eval_proj_multipliers (rvec y, real_t M) const

const Box &	get_box_C () const

const Box &	get_box_D () const

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

void	check () const

Static Public Member Functions
static real_t	eval_proj_grad_step_box (const Box &C, real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p)
	Projected gradient step for rectangular box C.

static void	eval_prox_grad_step_box_l1_impl (const Box &C, const auto &λ, real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p)
	Proximal gradient step for rectangular box C with ℓ₁-regularization.

static real_t	eval_prox_grad_step_box_l1 (const Box &C, const auto &λ, real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p)
	Proximal gradient step for rectangular box C with ℓ₁-regularization.

static real_t	eval_prox_grad_step_box_l1_scal (const Box &C, real_t λ, real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p)
	Proximal gradient step for rectangular box C with ℓ₁-regularization.

static void	eval_proj_multipliers_box (const Box &D, rvec y, real_t M, index_t penalty_alm_split)

Public Attributes
length_t	n
	Number of decision variables, dimension of x.

length_t	m
	Number of constraints, dimension of g(x) and z.

Box	C {this->n}
	Constraints of the decision variables, \( x \in C \).

Box	D {this->m}
	Other constraints, \( g(x) \in D \).

vec	l1_reg {}
	\( \ell_1 \) (1-norm) regularization parameter.

index_t	penalty_alm_split = 0
	Components of the constraint function with indices below this number are handled using a quadratic penalty method rather than using an augmented Lagrangian method.

Member Typedef Documentation

◆ Box

template<Config Conf>

using Box = alpaqa::Box<config_t>

Definition at line 19 of file box-constr-problem.hpp.

Constructor & Destructor Documentation

◆ BoxConstrProblem() [1/4]

template<Config Conf>

BoxConstrProblem	(	length_t	n,
		length_t	m
	)

inline

Create a problem with inactive boxes \( (-\infty, +\infty) \), with no \( \ell_1 \)-regularization, and all general constraints handled using ALM.

Parameters

n	Number of decision variables
m	Number of constraints

Definition at line 29 of file box-constr-problem.hpp.

◆ BoxConstrProblem() [2/4]

template<Config Conf>

BoxConstrProblem	(	Box	C,
		Box	D,
		vec	l1_reg = `vec(0)`,
		index_t	penalty_alm_split = `0`
	)

inline

Definition at line 33 of file box-constr-problem.hpp.

◆ BoxConstrProblem() [3/4]

template<Config Conf>

BoxConstrProblem ( const BoxConstrProblem< Conf > & )

default

◆ BoxConstrProblem() [4/4]

template<Config Conf>

BoxConstrProblem ( BoxConstrProblem< Conf > && )

defaultnoexcept

Member Function Documentation

◆ resize()

template<Config Conf>

void resize	(	length_t	n,
		length_t	m
	)

inline

Change the dimensions of the problem (number of decision variables and number of constaints).

Destructive: resizes and/or resets the members C, D, l1_reg and penalty_alm_split.

Definition at line 41 of file box-constr-problem.hpp.

◆ operator=() [1/2]

template<Config Conf>

BoxConstrProblem & operator= ( const BoxConstrProblem< Conf > & )

default

◆ operator=() [2/2]

template<Config Conf>

BoxConstrProblem & operator= ( BoxConstrProblem< Conf > && )

defaultnoexcept

◆ get_n()

template<Config Conf>

length_t get_n ( ) const

inline

Number of decision variables, n.

Definition at line 75 of file box-constr-problem.hpp.

◆ get_m()

template<Config Conf>

length_t get_m ( ) const

inline

Number of constraints, m.

Definition at line 77 of file box-constr-problem.hpp.

◆ eval_proj_grad_step_box()

template<Config Conf>

static real_t eval_proj_grad_step_box	(	const Box &	C,
		real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rvec	x̂,
		rvec	p
	)

inlinestatic

Projected gradient step for rectangular box C.

\[ \begin{aligned} \hat x &= \Pi_C(x - \gamma\nabla\psi(x)) \\ p &= \hat x - x \\ &= \max(\underline x - x, \;\min(-\gamma\nabla\psi(x), \overline x - x) \end{aligned} \]

Definition at line 84 of file box-constr-problem.hpp.

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◆ eval_prox_grad_step_box_l1_impl()

template<Config Conf>

static void eval_prox_grad_step_box_l1_impl	(	const Box &	C,
		const auto &	λ,
		real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rvec	x̂,
		rvec	p
	)

inlinestatic

Proximal gradient step for rectangular box C with ℓ₁-regularization.

\[ \begin{aligned} h(x) &= \|x\|_1 + \delta_C(x) \\ \hat x &= \prox_{\gamma h}(x - \gamma\nabla\psi(x)) \\ &= -\max\big( x - \overline x, \;\min\big( x - \underline x, \;\min\big( \gamma(\nabla\psi(x) + \lambda), \;\max\big( \gamma(\nabla\psi(x) - \lambda), x \big) \big) \big) \big) \end{aligned} \]

Definition at line 107 of file box-constr-problem.hpp.

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◆ eval_prox_grad_step_box_l1()

template<Config Conf>

static real_t eval_prox_grad_step_box_l1	(	const Box &	C,
		const auto &	λ,
		real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rvec	x̂,
		rvec	p
	)

inlinestatic

Proximal gradient step for rectangular box C with ℓ₁-regularization.

\[ \begin{aligned} h(x) &= \|x\|_1 + \delta_C(x) \\ \hat x &= \prox_{\gamma h}(x - \gamma\nabla\psi(x)) \\ &= -\max\big( x - \overline x, \;\min\big( x - \underline x, \;\min\big( \gamma(\nabla\psi(x) + \lambda), \;\max\big( \gamma(\nabla\psi(x) - \lambda), x \big) \big) \big) \big) \end{aligned} \]

Definition at line 116 of file box-constr-problem.hpp.

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◆ eval_prox_grad_step_box_l1_scal()

template<Config Conf>

static real_t eval_prox_grad_step_box_l1_scal	(	const Box &	C,
		real_t	λ,
		real_t	γ,
		crvec	x,
		crvec	grad_ψ,
		rvec	x̂,
		rvec	p
	)

inlinestatic

Proximal gradient step for rectangular box C with ℓ₁-regularization.

\[ \begin{aligned} h(x) &= \|x\|_1 + \delta_C(x) \\ \hat x &= \prox_{\gamma h}(x - \gamma\nabla\psi(x)) \\ &= -\max\big( x - \overline x, \;\min\big( x - \underline x, \;\min\big( \gamma(\nabla\psi(x) + \lambda), \;\max\big( \gamma(\nabla\psi(x) - \lambda), x \big) \big) \big) \big) \end{aligned} \]

Definition at line 123 of file box-constr-problem.hpp.

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◆ eval_prox_grad_step()

template<Config Conf>

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

inline

See also: TypeErasedProblem::eval_prox_grad_step

Definition at line 132 of file box-constr-problem.hpp.

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◆ eval_proj_diff_g()

template<Config Conf>

void eval_proj_diff_g	(	crvec	z,
		rvec	p
	)		const

inline

See also: TypeErasedProblem::eval_proj_diff_g

Definition at line 142 of file box-constr-problem.hpp.

◆ eval_proj_multipliers_box()

template<Config Conf>

static void eval_proj_multipliers_box	(	const Box &	D,
		rvec	y,
		real_t	M,
		index_t	penalty_alm_split
	)

inlinestatic

Definition at line 144 of file box-constr-problem.hpp.

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◆ eval_proj_multipliers()

template<Config Conf>

void eval_proj_multipliers	(	rvec	y,
		real_t	M
	)		const

inline

See also: TypeErasedProblem::eval_proj_multipliers

Definition at line 166 of file box-constr-problem.hpp.

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◆ get_box_C()

template<Config Conf>

const Box & get_box_C ( ) const

inline

See also: TypeErasedProblem::get_box_C

Definition at line 171 of file box-constr-problem.hpp.

◆ get_box_D()

template<Config Conf>

const Box & get_box_D ( ) const

inline

See also: TypeErasedProblem::get_box_D

Definition at line 173 of file box-constr-problem.hpp.

◆ eval_inactive_indices_res_lna()

template<Config Conf>

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

inline

See also: TypeErasedProblem::eval_inactive_indices_res_lna

Definition at line 176 of file box-constr-problem.hpp.

◆ check()

template<Config Conf>

void check ( ) const

inline

See also: TypeErasedProblem::check

Definition at line 213 of file box-constr-problem.hpp.

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Member Data Documentation

◆ n

template<Config Conf>

length_t n

Number of decision variables, dimension of x.

Examples: C++/CustomCppProblem/main.cpp.

Definition at line 22 of file box-constr-problem.hpp.

◆ m

template<Config Conf>

length_t m

Number of constraints, dimension of g(x) and z.

Examples: C++/CustomCppProblem/main.cpp.

Definition at line 24 of file box-constr-problem.hpp.

◆ C

template<Config Conf>

Box C {this->n}

Constraints of the decision variables, \( x \in C \).

Examples: C++/CasADi/Rosenbrock/main.cpp.

Definition at line 59 of file box-constr-problem.hpp.

◆ D

template<Config Conf>

Box D {this->m}

Other constraints, \( g(x) \in D \).

Definition at line 61 of file box-constr-problem.hpp.

◆ l1_reg

template<Config Conf>

vec l1_reg {}

\( \ell_1 \) (1-norm) regularization parameter.

Possible dimensions are: \( 0 \) (no regularization), \( 1 \) (a single scalar factor), or \( n \) (a different factor for each variable).

Definition at line 66 of file box-constr-problem.hpp.

◆ penalty_alm_split

template<Config Conf>

index_t penalty_alm_split = 0

Components of the constraint function with indices below this number are handled using a quadratic penalty method rather than using an augmented Lagrangian method.

Specifically, the Lagrange multipliers for these components (which determine the shifts in ALM) are kept at zero.

Definition at line 72 of file box-constr-problem.hpp.

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

src/alpaqa/include/alpaqa/problem/box-constr-problem.hpp

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Member Typedef Documentation

◆ Box

Constructor & Destructor Documentation

◆ BoxConstrProblem() [1/4]

◆ BoxConstrProblem() [2/4]

◆ BoxConstrProblem() [3/4]

◆ BoxConstrProblem() [4/4]

Member Function Documentation

◆ resize()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ get_n()

◆ get_m()

◆ eval_proj_grad_step_box()

◆ eval_prox_grad_step_box_l1_impl()

◆ eval_prox_grad_step_box_l1()

◆ eval_prox_grad_step_box_l1_scal()

◆ eval_prox_grad_step()

◆ eval_proj_diff_g()

◆ eval_proj_multipliers_box()

◆ eval_proj_multipliers()

◆ get_box_C()

◆ get_box_D()

◆ eval_inactive_indices_res_lna()

◆ check()

Member Data Documentation

◆ n

◆ m

◆ C

◆ D

◆ l1_reg

◆ penalty_alm_split