#include <alpaqa/util/problem.hpp>

Detailed Description

Problem description for minimization problems.

\[ \begin{aligned} & \underset{x}{\text{minimize}} & & f(x) &&&& f : \mathbb{R}^n \rightarrow \mathbb{R} \\ & \text{subject to} & & \underline{x} \le x \le \overline{x} \\ &&& \underline{z} \le g(x) \le \overline{z} &&&& g : \mathbb{R}^n \rightarrow \mathbb{R}^m \end{aligned} \]

Examples: CUTEst/Rosenbrock/main.cpp, and CasADi/Rosenbrock/main.cpp.

Definition at line 26 of file include/alpaqa/util/problem.hpp.

Inheritance diagram for Problem:

Collaboration diagram for Problem:

Public Types
using	f_sig = real_t(crvec x)
	Signature of the function that evaluates the cost \( f(x) \). More...

using	grad_f_sig = void(crvec x, rvec grad_fx)
	Signature of the function that evaluates the gradient of the cost function \( \nabla f(x) \). More...

using	g_sig = void(crvec x, rvec gx)
	Signature of the function that evaluates the constraints \( g(x) \). More...

using	grad_g_prod_sig = void(crvec x, crvec y, rvec grad_gxy)
	Signature of the function that evaluates the gradient of the constraints times a vector \( \nabla g(x)\ y \). More...

using	grad_gi_sig = void(crvec x, unsigned i, rvec grad_gi)
	Signature of the function that evaluates the gradient of one specific constraints \( \nabla g_i(x) \). More...

using	hess_L_prod_sig = void(crvec x, crvec y, crvec v, rvec Hv)
	Signature of the function that evaluates the Hessian of the Lagrangian multiplied by a vector \( \nabla_{xx}^2L(x, y)\ v \). More...

using	hess_L_sig = void(crvec x, crvec y, rmat H)
	Signature of the function that evaluates the Hessian of the Lagrangian \( \nabla_{xx}^2L(x, y) \). More...

Public Member Functions
	Problem ()=default

	Problem (unsigned int n, unsigned int m)

	Problem (unsigned n, unsigned int m, Box C, Box D, std::function< f_sig > f, std::function< grad_f_sig > grad_f, std::function< g_sig > g, std::function< grad_g_prod_sig > grad_g_prod, std::function< grad_gi_sig > grad_gi, std::function< hess_L_prod_sig > hess_L_prod, std::function< hess_L_sig > hess_L)

Public Attributes
unsigned int	n
	Number of decision variables, dimension of x. More...

unsigned int	m
	Number of constraints, dimension of g(x) and z. More...

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

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

std::function< f_sig >	f
	Cost function \( f(x) \). More...

std::function< grad_f_sig >	grad_f
	Gradient of the cost function \( \nabla f(x) \). More...

std::function< g_sig >	g
	Constraint function \( g(x) \). More...

std::function< grad_g_prod_sig >	grad_g_prod
	Gradient of the constraint function times vector \( \nabla g(x)\ y \). More...

std::function< grad_gi_sig >	grad_gi
	Gradient of a specific constraint \( \nabla g_i(x) \). More...

std::function< hess_L_prod_sig >	hess_L_prod
	Hessian of the Lagrangian function times vector \( \nabla_{xx}^2 L(x, y)\ v \). More...

std::function< hess_L_sig >	hess_L
	Hessian of the Lagrangian function \( \nabla_{xx}^2 L(x, y) \). More...

Member Typedef Documentation

◆ f_sig

using f_sig = real_t(crvec x)

Signature of the function that evaluates the cost \( f(x) \).

Parameters

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

Definition at line 35 of file include/alpaqa/util/problem.hpp.

◆ grad_f_sig

using grad_f_sig = void(crvec x, rvec grad_fx)

Signature of the function that evaluates the gradient of the cost function \( \nabla f(x) \).

Parameters

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

Definition at line 42 of file include/alpaqa/util/problem.hpp.

◆ g_sig

using g_sig = void(crvec x, rvec gx)

Signature of the function that evaluates the constraints \( g(x) \).

Parameters

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

Definition at line 48 of file include/alpaqa/util/problem.hpp.

◆ grad_g_prod_sig

using grad_g_prod_sig = void(crvec x, crvec y, rvec grad_gxy)

Signature of the function that evaluates the gradient of the constraints times a vector \( \nabla g(x)\ y \).

Parameters

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

Definition at line 59 of file include/alpaqa/util/problem.hpp.

◆ grad_gi_sig

using grad_gi_sig = void(crvec x, unsigned i, rvec grad_gi)

Signature of the function that evaluates the gradient of one specific constraints \( \nabla g_i(x) \).

Parameters

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

Definition at line 70 of file include/alpaqa/util/problem.hpp.

◆ hess_L_prod_sig

using hess_L_prod_sig = void(crvec x, crvec y, crvec v, rvec Hv)

Signature of the function that evaluates the Hessian of the Lagrangian multiplied by a vector \( \nabla_{xx}^2L(x, y)\ v \).

Parameters

[in]	x	Decision variable \( x \in \mathbb{R}^n \)
[in]	y	Lagrange multipliers \( y \in \mathbb{R}^m \)
[in]	v	Vector to multiply by \( v \in \mathbb{R}^n \)
[out]	Hv	Hessian-vector product \( \nabla_{xx}^2 L(x, y)\ v \in \mathbb{R}^{n} \)

Definition at line 83 of file include/alpaqa/util/problem.hpp.

◆ hess_L_sig

using hess_L_sig = void(crvec x, crvec y, rmat H)

Signature of the function that evaluates the Hessian of the Lagrangian \( \nabla_{xx}^2L(x, y) \).

Parameters

[in]	x	Decision variable \( x \in \mathbb{R}^n \)
[in]	y	Lagrange multipliers \( y \in \mathbb{R}^m \)
[out]	H	Hessian \( \nabla_{xx}^2 L(x, y) \in \mathbb{R}^{n\times n} \)

Definition at line 92 of file include/alpaqa/util/problem.hpp.

Constructor & Destructor Documentation

◆ Problem() [1/3]

Problem ( )

default

◆ Problem() [2/3]

Problem	(	unsigned int	n,
		unsigned int	m
	)

inline

Definition at line 111 of file include/alpaqa/util/problem.hpp.

◆ Problem() [3/3]

Problem	(	unsigned	n,
		unsigned int	m,
		Box	C,
		Box	D,
		std::function< f_sig >	f,
		std::function< grad_f_sig >	grad_f,
		std::function< g_sig >	g,
		std::function< grad_g_prod_sig >	grad_g_prod,
		std::function< grad_gi_sig >	grad_gi,
		std::function< hess_L_prod_sig >	hess_L_prod,
		std::function< hess_L_sig >	hess_L
	)