\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.1 - Linear and Quadratic Programming Solver
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CGAL::Nonnegative_quadratic_program_from_iterators< A_it, B_it, R_it, D_it, C_it > Class Template Reference
Linear and Quadratic Programming Solver Reference » Classes

#include <CGAL/QP_models.h>

Definition

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

\( \newcommand{\qprel}{\gtreqless} \newcommand{\qpx}{\mathbf{x}} \newcommand{\qpl}{\mathbf{l}} \newcommand{\qpu}{\mathbf{u}} \newcommand{\qpc}{\mathbf{c}} \newcommand{\qpb}{\mathbf{b}} \newcommand{\qpy}{\mathbf{y}} \newcommand{\qpw}{\mathbf{w}} \newcommand{\qplambda}{\mathbf{\lambda}} \)

\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:

QuadraticProgram

NonnegativeQuadraticProgram

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

See also
NonnegativeQuadraticProgram
Quadratic_program<NT>
Quadratic_program_from_mps<NT>
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...
 

Constructor & Destructor Documentation

◆ Nonnegative_quadratic_program_from_iterators()

template<typename A_it , typename B_it , typename R_it , typename D_it , typename C_it >
CGAL::Nonnegative_quadratic_program_from_iterators< A_it, B_it, R_it, D_it, C_it >::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.

The passed iterators are merely stored, no copying of the program data takes place. How these iterators are supposed to encode the nonnegative quadratic program is described in NonnegativeQuadraticProgram.