Problem Class Reference

#include <alpaqa/util/problem.hpp>

Detailed Description

Problem description for minimization problems.

$$\begin{array}{rlrlrlrl}& \underset{x}{\text{minimize}}& & f(x)& & & & f:{\mathbb{R}}^n\to \mathbb{R}\\ & \text{subject to}& & \underset{―}{x}\le x\le \bar{x}\\ & & & \underset{―}{z}\le g(x)\le \bar{z}& & & & g:{\mathbb{R}}^n\to {\mathbb{R}}^m\end{array}$$

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 $\mathrm{\nabla }f(x)$. 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 $\mathrm{\nabla }g(x)y$. 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 $\mathrm{\nabla }{g}_i(x)$. 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 ${\mathrm{\nabla }}_{xx}^{2}L(x,y)v$. More...
using	hess_L_sig = void(crvec x, crvec y, rmat H)
	Signature of the function that evaluates the Hessian of the Lagrangian ${\mathrm{\nabla }}_{xx}^{2}L(x,y)$. 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 $\mathrm{\nabla }f(x)$. 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 $\mathrm{\nabla }g(x)y$. More...
std::function< grad_gi_sig >	grad_gi
	Gradient of a specific constraint $\mathrm{\nabla }{g}_i(x)$. More...
std::function< hess_L_prod_sig >	hess_L_prod
	Hessian of the Lagrangian function times vector ${\mathrm{\nabla }}_{xx}^{2}L(x,y)v$. More...
std::function< hess_L_sig >	hess_L
	Hessian of the Lagrangian function ${\mathrm{\nabla }}_{xx}^{2}L(x,y)$. 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 $\mathrm{\nabla }f(x)$.

Parameters

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

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 $\mathrm{\nabla }g(x)y$.

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 $\mathrm{\nabla }g(x)y\in {\mathbb{R}}^n$

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 $\mathrm{\nabla }{g}_i(x)$.

Parameters

[in]	x	Decision variable $x\in {\mathbb{R}}^n$
[in]	i	Which constraint $0\le i<m$
[out]	grad_gi	Gradient of the constraint $\mathrm{\nabla }{g}_i(x){\mathbb{R}}^n$

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 ${\mathrm{\nabla }}_{xx}^{2}L(x,y)v$.

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 ${\mathrm{\nabla }}_{xx}^{2}L(x,y)v\in {\mathbb{R}}^n$

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 ${\mathrm{\nabla }}_{xx}^{2}L(x,y)$.

Parameters

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

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  )

inline

Definition at line 114 of file include/alpaqa/util/problem.hpp.

Member Data Documentation

n

unsigned int n

Number of decision variables, dimension of x.

Definition at line 27 of file include/alpaqa/util/problem.hpp.

m

unsigned int m

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

Definition at line 28 of file include/alpaqa/util/problem.hpp.

C

Box C

Constraints of the decision variables, $x\in C$.

Definition at line 29 of file include/alpaqa/util/problem.hpp.

D

Box D

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

Definition at line 30 of file include/alpaqa/util/problem.hpp.

f

std::function<f_sig> f

Cost function $f(x)$.

Definition at line 95 of file include/alpaqa/util/problem.hpp.

grad_f

std::function<grad_f_sig> grad_f

Gradient of the cost function $\mathrm{\nabla }f(x)$.

Definition at line 97 of file include/alpaqa/util/problem.hpp.

g

std::function<g_sig> g

Constraint function $g(x)$.

Definition at line 99 of file include/alpaqa/util/problem.hpp.

grad_g_prod

std::function<grad_g_prod_sig> grad_g_prod

Gradient of the constraint function times vector $\mathrm{\nabla }g(x)y$.

Definition at line 101 of file include/alpaqa/util/problem.hpp.

grad_gi

std::function<grad_gi_sig> grad_gi

Gradient of a specific constraint $\mathrm{\nabla }{g}_i(x)$.

Definition at line 103 of file include/alpaqa/util/problem.hpp.

hess_L_prod

std::function<hess_L_prod_sig> hess_L_prod

Hessian of the Lagrangian function times vector ${\mathrm{\nabla }}_{xx}^{2}L(x,y)v$.

Definition at line 106 of file include/alpaqa/util/problem.hpp.

hess_L

std::function<hess_L_sig> hess_L

Hessian of the Lagrangian function ${\mathrm{\nabla }}_{xx}^{2}L(x,y)$.

Definition at line 108 of file include/alpaqa/util/problem.hpp.

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

• include/alpaqa/util/problem.hpp