CGAL 5.1.3 - Linear and Quadratic Programming Solver
CGAL::Nonnegative_quadratic_program_from_iterators< A_it, B_it, R_it, D_it, C_it > Class Template Reference

#include <CGAL/QP_models.h>

## Definition

An object of class Nonnegative_quadratic_program_from_iterators describes a convex quadratic program of the form.

\begin{eqnarray*} \mbox{(QP)}& \mbox{minimize} & \qpx^{T}D\qpx+\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 $$\{\leq, =, \geq\}$$,

• $$D$$ is a symmetric positive-semidefinite $$n\times n$$ matrix (the quadratic objective function),

• $$\qpc$$ is an $$n$$-dimensional vector (the linear objective function), and
• $$c_0$$ is a constant.

This class is simply a wrapper for existing iterators, and it does not copy the program data.

It frequently happens that all values in one of the vectors from above are the same, for example if the system $$Ax\qprel b$$ is actually a system of equations $$Ax=b$$. To get an iterator over such a vector, it is not necessary to store multiple copies of the value in some container; an instance of the class Const_oneset_iterator<T>, constructed from the value in question, does the job more efficiently.

Is Model Of:

Example

QP_solver/first_nonnegative_qp_from_iterators.cpp

The following example for the simpler model Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it> should give you a flavor of the use of this model in practice.

QP_solver/solve_convex_hull_containment_lp.h

QP_solver/convex_hull_containment.cpp

Examples:
QP_solver/first_nonnegative_qp_from_iterators.cpp.

## Creation

Nonnegative_quadratic_program_from_iterators (int n, int m, const A_it &a, const B_it &b, const R_it &r, const D_it &d, const C_it &c, const std::iterator_traits< C_it >value_type &c0=0)
constructs qp from given random-access iterators and the constant c0. More...