BoxConstrProblem< Conf > Class Template Reference

#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 $(-\mathrm{\infty },+\mathrm{\infty })$, with no ${\ell }_1$-regularization, and all general constraints handled using ALM.
	BoxConstrProblem (std::tuple< length_t, length_t > dims)
	Create a problem with inactive boxes $(-\mathrm{\infty },+\mathrm{\infty })$, 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
bool	provides_get_box_C () const
	Only supported if the ℓ₁-regularization term is zero.
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() [1/5]

template<Config Conf>

BoxConstrProblem ( length_t  n, length_t  m  )

inline

Create a problem with inactive boxes $(-\mathrm{\infty },+\mathrm{\infty })$, 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() [2/5]

template<Config Conf>

BoxConstrProblem ( std::tuple< length_t, length_t >  dims )

inline

Create a problem with inactive boxes $(-\mathrm{\infty },+\mathrm{\infty })$, with no ${\ell }_1$-regularization, and all general constraints handled using ALM.

Parameters

dims	Number of variables and number of constraints.

Definition at line 34 of file box-constr-problem.hpp.

BoxConstrProblem() [3/5]

template<Config Conf>

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

inline

Definition at line 37 of file box-constr-problem.hpp.

BoxConstrProblem() [4/5]

template<Config Conf>

BoxConstrProblem ( const BoxConstrProblem< Conf > &  )

default

BoxConstrProblem() [5/5]

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.

Parameters

n	Number of decision variables
m	Number of constraints

Definition at line 45 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 81 of file box-constr-problem.hpp.

get_m()

template<Config Conf>

length_t get_m ( ) const

inline

Number of constraints, m.

Definition at line 83 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.

$$\begin{array}{rl}\hat{x}& ={\mathrm{\Pi }}_C(x-\gamma \mathrm{\nabla }\psi (x))\\ p& =\hat{x}-x\\ & =max(\underset{―}{x}-x,min(-\gamma \mathrm{\nabla }\psi (x),\bar{x}-x)\end{array}$$

Definition at line 90 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.

$$\begin{array}{rl}h(x)& =\Vert x{\Vert }_1+{\delta }_C(x)\\ \hat{x}& ={\mathbf{prox}}_{\gamma h}(x-\gamma \mathrm{\nabla }\psi (x))\\ & =-max(x-\bar{x},min(x-\underset{―}{x},min(\gamma (\mathrm{\nabla }\psi (x)+\lambda ),max(\gamma (\mathrm{\nabla }\psi (x)-\lambda ),x))))\end{array}$$

Definition at line 113 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.

$$\begin{array}{rl}h(x)& =\Vert x{\Vert }_1+{\delta }_C(x)\\ \hat{x}& ={\mathbf{prox}}_{\gamma h}(x-\gamma \mathrm{\nabla }\psi (x))\\ & =-max(x-\bar{x},min(x-\underset{―}{x},min(\gamma (\mathrm{\nabla }\psi (x)+\lambda ),max(\gamma (\mathrm{\nabla }\psi (x)-\lambda ),x))))\end{array}$$

Definition at line 122 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.

$$\begin{array}{rl}h(x)& =\Vert x{\Vert }_1+{\delta }_C(x)\\ \hat{x}& ={\mathbf{prox}}_{\gamma h}(x-\gamma \mathrm{\nabla }\psi (x))\\ & =-max(x-\bar{x},min(x-\underset{―}{x},min(\gamma (\mathrm{\nabla }\psi (x)+\lambda ),max(\gamma (\mathrm{\nabla }\psi (x)-\lambda ),x))))\end{array}$$

Definition at line 129 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 138 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 148 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 150 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 172 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 177 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 179 of file box-constr-problem.hpp.

provides_get_box_C()

template<Config Conf>

bool provides_get_box_C ( ) const

inline

Only supported if the ℓ₁-regularization term is zero.

See also

TypeErasedProblem::provides_get_box_C

Definition at line 183 of file box-constr-problem.hpp.

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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 189 of file box-constr-problem.hpp.

check()

template<Config Conf>

void check ( ) const

inline

See also

TypeErasedProblem::check

Definition at line 226 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 65 of file box-constr-problem.hpp.

D

template<Config Conf>

Box D {this->m}

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

Definition at line 67 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 72 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 78 of file box-constr-problem.hpp.

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

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