mirror of https://github.com/CGAL/cgal
164 lines
4.2 KiB
C++
164 lines
4.2 KiB
C++
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/*!
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\ingroup PkgQPSolverConcepts
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\cgalConcept
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A model of `NonnegativeQuadraticProgram` describes a convex quadratic program of the form
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\f{eqnarray*}{
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\mbox{(QP)}& \mbox{minimize}
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& \qpx^{T}D\qpx+\qpc^{T}\qpx+c_0 \\
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&\mbox{subject to} & A\qpx\qprel \qpb, \\
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& & \qpx \geq 0
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\f}
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in \f$ n\f$ real variables \f$ \qpx=(x_0,\ldots,x_{n-1})\f$.
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Here,
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<UL>
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<LI>\f$ A\f$ is an \f$ m\times n\f$ matrix (the constraint matrix),
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<LI>\f$ \qpb\f$ is an \f$ m\f$-dimensional vector (the right-hand side),
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<LI>\f$ \qprel\f$ is an \f$ m\f$-dimensional vector of relations
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from \f$ \{\leq, =, \geq\}\f$,
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<LI>\f$ D\f$ is a symmetric positive-semidefinite \f$ n\times n\f$ matrix (the
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quadratic objective function),
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<LI>\f$ \qpc\f$ is an \f$ n\f$-dimensional vector (the linear objective
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function), and
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<LI>\f$ c_0\f$ is a constant.
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</UL>
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The description is given by appropriate <I>random-access</I>
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iterators over the program data, see below. The program therefore
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comes in <I>dense</I> representation which includes zero entries.
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\cgalHasModelsBegin
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\cgalHasModels{CGAL::Quadratic_program<NT>}
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\cgalHasModels{CGAL::Quadratic_program_from_mps<NT>}
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\cgalHasModels{CGAL::Nonnegative_quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>}
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\cgalHasModelsEnd
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The value types of all iterator types (nested iterator
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types, respectively, for `A_iterator` and `D_iterator`) must be
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convertible to some common `IntegralDomain` `ET`.
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\sa `QuadraticProgram`
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\sa `LinearProgram`
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\sa `NonnegativeLinearProgram`
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*/
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class NonnegativeQuadraticProgram {
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public:
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/// \name Types
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/// @{
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/*!
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A random access iterator type to go
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columnwise over the constraint matrix \f$ A\f$. The value type
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is a random access iterator type for an individual column that
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goes over the entries in that column.
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*/
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typedef unspecified_type A_iterator;
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/*!
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A random access iterator type to go over
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the entries of the right-hand side \f$ \qpb\f$.
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*/
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typedef unspecified_type B_iterator;
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/*!
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A random access iterator type to go over the
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relations \f$ \qprel\f$. The value type of `R_iterator` is
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`CGAL::Comparison_result`.
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*/
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typedef unspecified_type R_iterator;
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/*!
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A random access iterator type to go rowwise
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over the matrix \f$ 2D\f$. The value type
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is a random access iterator type for an individual row that
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goes over the entries in that row, up to (and including) the
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entry on the main diagonal.
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*/
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typedef unspecified_type D_iterator;
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/*!
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A random access iterator type to go over the
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entries of the linear objective function vector \f$ c\f$.
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*/
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typedef unspecified_type C_iterator;
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/// @}
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/// \name Operations
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/// @{
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/*!
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returns the number \f$ n\f$ of variables (number
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of columns of \f$ A\f$) in `qp`.
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*/
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int get_n() const;
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/*!
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returns the number \f$ m\f$ of constraints
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(number of rows of \f$ A\f$) in `qp`.
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*/
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int get_m() const;
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/*!
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returns an iterator over the columns
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of \f$ A\f$. The corresponding past-the-end iterator is `get_a()+get_n()`.
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For \f$ j=0,\ldots,n-1\f$, `*(get_a()+j)` is a random access
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iterator for column \f$ j\f$.
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*/
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A_iterator get_a() const;
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/*!
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returns an iterator over the entries
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of \f$ \qpb\f$. The corresponding past-the-end iterator is
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`get_b()+get_m()`.
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*/
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B_iterator get_b() const;
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/*!
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returns an iterator over the entries
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of \f$ \qprel\f$. The corresponding past-the-end iterator is
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`get_r()+get_m()`.
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The value `CGAL::SMALLER` stands
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for \f$ \leq\f$, `CGAL::EQUAL` stands for \f$ =\f$, and `CGAL::LARGER`
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stands for \f$ \geq\f$.
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*/
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R_iterator get_r() const;
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/*!
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returns an iterator over the rows of
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\f$ 2D\f$. The corresponding past-the-end iterator is `get_d()+get_n()`.
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For \f$ i=0,\ldots,n-1\f$, `*(get_d()+i)` is a random access
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iterator for the entries in row \f$ i\f$ <I>below or on the diagonal</I>.
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The valid range of this iterator is
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guaranteed to have length \f$ i+1\f$ but not more. Values to the right
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of the diagonal are deduced from the symmetry requirement on \f$ D\f$.
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*/
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D_iterator get_d() const;
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/*!
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returns an iterator over the entries
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of \f$ \qpc\f$. The corresponding past-the-end iterator is
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`get_c()+get_n()`.
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*/
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C_iterator get_c() const;
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/*!
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returns the constant term \f$ c_0\f$ of the objective function.
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*/
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std::iterator_traits<C_iterator>::value_type get_c0() const;
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/// @}
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}; /* end NonnegativeQuadraticProgram */
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