NonnegativeLinearProgram

Definition

(QP)$$	minimize$$	cTx+c0
	subject to$$	Ax ~ b,
		x 0

in $$n real variables $$x=(x₀,...,x_n-1). Here,

• $$A is an $$m × n matrix (the constraint matrix),
• $$b is an $$m-dimensional vector (the right-hand side),
• $$ ~  is an $$m-dimensional vector of relations from $${ , =, },
• $$c is an $$n-dimensional vector (the linear objective function), and
• $$c₀ 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

Types

Operations

int	lp.get_n ()	returns the number $$n of variables (number of columns of $$A) in lp.
int	lp.get_m ()	returns the number $$m of constraints (number of rows of $$A) in lp.
A_iterator	lp.get_a ()	returns an iterator over the columns of $$A. The corresponding past-the-end iterator is get_a()+get_n(). For $$j=0,...,n-1, $$*(get_a()+j) is a random access iterator for column $$j.
B_iterator	lp.get_b ()	returns an iterator over the entries of $$b. The corresponding past-the-end iterator is get_b()+get_m().
R_iterator	lp.get_r ()	returns an iterator over the entries of $$ ~ . The corresponding past-the-end iterator is get_r()+get_m(). The value CGAL::SMALLER stands for $$ , CGAL::EQUAL stands for $$=, and CGAL::LARGER stands for $$ .
C_iterator	lp.get_c ()	returns an iterator over the entries of $$c. The corresponding past-the-end iterator is get_c()+get_n().
std::iterator_traits<C_iterator>::value_type
	lp.get_c0 ()	returns the constant term $$c0 of the objective function.

Requirements

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

See Also

Quadratic_program<NT>
Quadratic_program_from_mps<NT>
Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it>

and the other concepts

QuadraticProgram
LinearProgram
NonnegativeQuadraticProgram