NonnegativeLinearProgram

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NonnegativeLinearProgram

Definition

A model of NonnegativeLinearProgram describes a linear program of the form

(QP)	minimize	c^Tx+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

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

Types

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.

NonnegativeLinearProgram::B_iterator
	A random access iterator type to go over the entries of the right-hand side b.

NonnegativeLinearProgram::R_iterator
	A random access iterator type to go over the relations ⋛ . The value type of R_iterator is CGAL::Comparison_result.

NonnegativeLinearProgram::C_iterator
	A random access iterator type to go over the entries of the linear objective function vector c.

Operations

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

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

A_iterator	lp.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, … ,n-1, *(get_a()+j) is a random access iterator for column j.

B_iterator	lp.get_b () const	returns an iterator over the entries of b. The corresponding past-the-end iterator is get_b()+get_m().

R_iterator	lp.get_r () const	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 () const	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 () const	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.