#include <Concepts/QuadraticProgramTraits.h>

Definition

A concept that describes the set of methods used to define and solve a quadratic programming (qp) problem of the general form:

\begin{eqnarray*} & \mbox{minimize} & \frac{1}{2}\mathbf{x}^{T}P\mathbf{x} + \mathbf{q}^{T}\mathbf{x} + r \\ & \mbox{subject to} & \mathbf{l} \leq A\mathbf{x} \leq \mathbf{u} \end{eqnarray*}

in \( n \) real variables \( \mathbf{x} = (x_0, \ldots, x_{n-1}) \) and \( m \) constraints.

Here,

\( P \) is a symmetric positive-semidefinite \( n \times n\) matrix (the quadratic objective function),
\( \mathbf{q} \) is an \( n \)-dimensional vector (the linear objective function),
\( r \) is a constant,
\( A \) is an \( m\times n\) matrix (the constraint matrix),
\( \mathbf{l} \) is an \( m \)-dimensional vector of lower constraint bounds, where \( l_i \in \mathbb{R} \cup \{-\infty\} \) for all \( i \),
\( \mathbf{u} \) is an \( m \)-dimensional vector of upper constraint bounds, where \( u_i \in \mathbb{R} \cup \{+\infty\} \) for all \( i \).

Has models
: CGAL::OSQP_quadratic_program_traits<T>

Memory
void	resize (const std::size_t n, const std::size_t m)
	Allocates memory for `n` variables and `m` constraints in `qp`.

Initialization
void	set_P (const std::size_t i, const std::size_t j, const FT value)
	Sets the entries `Pij` and `Pji` of `qp` to `value`.

void	set_q (const std::size_t i, const FT value)
	Sets the entry `qi` of `qp` to `value`.

void	set_r (const FT value)
	Sets the entry `r` of `qp` to `value`.

void	set_A (const std::size_t i, const std::size_t j, const FT value)
	Sets the entry `Aij` in the row `i` and column `j` of the constraint matrix `A` of `qp` to `value`.

void	set_l (const std::size_t i, const FT value)
	Sets the entry `li` of `qp` to `value`.

void	set_u (const std::size_t i, const FT value)
	Sets the entry `ui` of `qp` to `value`.

Solution
template<typename OutIterator >
bool	solve (OutIterator solution)
	solves the quadratic program.

Member Function Documentation

◆ resize()

void QuadraticProgramTraits::resize	(	const std::size_t	n,
		const std::size_t	m
	)

Allocates memory for n variables and m constraints in qp.

◆ set_A()

void QuadraticProgramTraits::set_A	(	const std::size_t	i,
		const std::size_t	j,
		const FT	value
	)

Sets the entry Aij in the row i and column j of the constraint matrix A of qp to value.

◆ set_l()

void QuadraticProgramTraits::set_l	(	const std::size_t	i,
		const FT	value
	)

Sets the entry li of qp to value.

◆ set_P()

void QuadraticProgramTraits::set_P	(	const std::size_t	i,
		const std::size_t	j,
		const FT	value
	)

Sets the entries Pij and Pji of qp to value.

◆ set_q()

void QuadraticProgramTraits::set_q	(	const std::size_t	i,
		const FT	value
	)

Sets the entry qi of qp to value.

◆ set_r()

void QuadraticProgramTraits::set_r ( const FT value )

Sets the entry r of qp to value.

◆ set_u()

void QuadraticProgramTraits::set_u	(	const std::size_t	i,
		const FT	value
	)

Sets the entry ui of qp to value.

◆ solve()

template<typename OutIterator >

bool QuadraticProgramTraits::solve ( OutIterator solution )

solves the quadratic program.

Number of values in solution equals to the number n of values in the vector x.

Template Parameters

OutIterator a model of OutputIterator that accepts values of type FieldNumberType

Parameters

solution an output iterator with the solution

Returns: a status of the computation success == true