Definition

A model of NonnegativeLinearProgram describes a linear program of the form.

$\begin{eqnarray*} \mbox{(QP)}& \mbox{minimize} &\qpc^{T}\qpx+c_0 \\ &\mbox{subject to} & A\qpx\qprel \qpb, \\ & & \qpx \geq 0 \end{eqnarray*}$

in $n$ real variables $\qpx=(x_0,\ldots,x_{n-1})$ . Here,

$A$ is an $m\times n$ matrix (the constraint matrix),
$\qpb$ is an $m$ -dimensional vector (the right-hand side),
$\qprel$ is an $m$ -dimensional vector of relations from $\{\leq, =, \geq\}$ ,
$\qpc$ is an $n$ -dimensional vector (the linear objective function), and
$c_0$ is a constant.

The description is given by appropriate random-access iterators over the program data, see below. The program therefore comes in dense representation which includes zero entries.

Has models
: CGAL::Quadratic_program<NT>
: CGAL::Quadratic_program_from_mps<NT>
: CGAL::Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>

The value types of all iterator types (nested iterator types, respectively, for A_iterator) must be convertible to some common IntegralDomain ET.

Has models
: CGAL::Quadratic_program<NT>
: CGAL::Quadratic_program_from_mps<NT>
: CGAL::Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it>

See also: QuadraticProgram; LinearProgram; NonnegativeQuadraticProgram

Types
typedef unspecified_type	A_iterator
	A random access iterator type to go columnwise over the constraint matrix $A$ .

typedef unspecified_type	B_iterator
	A random access iterator type to go over the entries of the right-hand side $\qpb$ .

typedef unspecified_type	R_iterator
	A random access iterator type to go over the relations $\qprel$ .

typedef unspecified_type	C_iterator
	A random access iterator type to go over the entries of the linear objective function vector $c$ .

Operations
int	get_n () const
	returns the number $n$ of variables (number of columns of $A$ ) in `lp`.

int	get_m () const
	returns the number $m$ of constraints (number of rows of $A$ ) in `lp`.

A_iterator	get_a () const
	returns an iterator over the columns of $A$ .

B_iterator	get_b () const
	returns an iterator over the entries of $\qpb$ .

R_iterator	get_r () const
	returns an iterator over the entries of $\qprel$ .

C_iterator	get_c () const
	returns an iterator over the entries of $\qpc$ .

std::iterator_traits< C_iterator >::value_type	get_c0 () const
	returns the constant term $c_0$ of the objective function.

Member Typedef Documentation

◆ A_iterator

typedef unspecified_type NonnegativeLinearProgram::A_iterator

A random access iterator type to go columnwise over the constraint matrix $A$ .

The value type is a random access iterator type for an individual column that goes over the entries in that column.

◆ R_iterator

typedef unspecified_type NonnegativeLinearProgram::R_iterator

A random access iterator type to go over the relations $\qprel$ .

The value type of R_iterator is CGAL::Comparison_result.

Member Function Documentation

◆ get_a()

A_iterator NonnegativeLinearProgram::get_a ( ) const

returns an iterator over the columns of $A$ .

The corresponding past-the-end iterator is get_a()+get_n(). For $j=0,\ldots,n-1$ , *(get_a()+j) a random access iterator for column $j$ .

◆ get_b()

B_iterator NonnegativeLinearProgram::get_b ( ) const

returns an iterator over the entries of $\qpb$ .

The corresponding past-the-end iterator is get_b()+get_m().

◆ get_c()

C_iterator NonnegativeLinearProgram::get_c ( ) const

returns an iterator over the entries of $\qpc$ .

The corresponding past-the-end iterator is get_c()+get_n().

◆ get_r()

R_iterator NonnegativeLinearProgram::get_r ( ) const

returns an iterator over the entries of $\qprel$ .

The corresponding past-the-end iterator is get_r()+get_m(). The value CGAL::SMALLER stands for $\leq$ , CGAL::EQUAL stands for $=$ , and CGAL::LARGER stands for $\geq$ .