LinearProgramTraits Concept Reference

Definition

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

\begin{eqnarray*} & \mbox{minimize} & \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,

• \( \mathbf{q} \) 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 \( i \).

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

Initialization
void	set_q (const std::size_t i, const FT value)
	Sets the entry qi of lp to value.
void	set_r (const FT value)
	Sets the entry r of lp 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 lp to value.
void	set_l (const std::size_t i, const FT value)
	Sets the entry li of lp to value.
void	set_u (const std::size_t i, const FT value)
	Sets the entry ui of lp to value.

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

Member Function Documentation

solve()

template<typename OutIterator >

bool LinearProgramTraits::solve

(

OutIterator

solution

)

solves the linear 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