CGAL::Quadratic_program<NT>

#include <CGAL/QP_models.h>

Definition

An object of class Quadratic_program<NT> describes a convex quadratic program of the form
(QP) minimize xTDx+cTx+c0
subject to Ax b,
l x u
in n real variables x=(x0, ,xn-1). Here,

If D=0, the program is a linear program; if the variable bounds are x 0, we have a nonnegative program.

This class allows you to build your program entry by entry, using the set-methods below.

If you only need to wrap existing (random-access) iterators over your own data, then you may use any of the four models Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>, Linear_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, C_it>, Nonnegative_quadratic_program_from_iterators<A_it, B_it, R_it, D_it, C_it>, and Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it>.

If you want to read a quadratic program in MPSFormat from a stream, please use the model Quadratic_program_from_mps<NT>.

Is Model for the Concepts

QuadraticProgram
LinearProgram
NonnegativeQuadraticProgram
NonnegativeLinearProgram

Types

Quadratic_program<NT>::NT
The number type of the program entries.

Creation

Quadratic_program<NT> qp ( CGAL::Comparison_result default_r = CGAL::EQUAL,
bool default_fl = true,
NT default_l = 0,
bool default_fu = false,
NT default_u = 0);
constructs a quadratic program with no variables and no constraints, ready for data to be added. Unless relations are explicitly set, they will be of type default_r. Unless bounds are explicitly set, they will be as specified by default_fl (finite lower bound?), default_l (lower bound value if lower bound is finite), default_fu (finite upper bound?), and default_l (upper bound value if upper bound is finite). If all parameters take their default values, we thus get equality constraints and bounds x 0 by default. Numerical entries that are not explicitly set will default to 0.
Precondition: if default_fl=default_fu=true, then default_l default_u

Operations

bool qp.is_linear () returns true if and only if qp is a linear program.

bool qp.is_nonnegative () returns true if and only if qp is a nonnegative program.

void qp.set_a ( int j, int i, NT val) sets the entry Aij in column j and row i of the constraint matrix A of qp to val. An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_b ( int i, NT val) sets the entry bi of qp to val. An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_r ( int i, CGAL::Comparison_result rel)
sets the entry i of qp to rel. CGAL::SMALLER means that the i-th constraint is of type `` '', CGAL::EQUAL means ``='', and CGAL::LARGER encodes `` ''. An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_l ( int j, bool is_finite, NT val = NT(0))
if is_finite, this sets the entry lj of qp to val, otherwise it sets lj to -∞. An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_u ( int j, bool is_finite, NT val = NT(0))
if is_finite, this sets the entry uj of qp to val, otherwise it sets uj to . An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_c ( int j, NT val) sets the entry cj of qp to val. An existing entry is overwritten. qp is enlarged if necessary to accomodate this entry.

void qp.set_c0 ( NT val) sets the entry c0 of qp to val. An existing entry is overwritten.

void qp.set_d ( int i, int j, NT val) sets the entries 2Dij and 2Dji of qp to val. Existing entries are overwritten. qp is enlarged if necessary to accomodate these entries.
Precondition: j <= i

Example

QP_solver/first_qp.cpp
QP_solver/first_lp.cpp
QP_solver/first_nonnegative_qp.cpp
QP_solver/first_nonnegative_lp.cpp
QP_solver/invert_matrix.cpp

See Also

Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>
Linear_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, C_it>
Nonnegative_quadratic_program_from_iterators<A_it, B_it, R_it, D_it, C_it>
Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it>
Quadratic_program_from_mps<NT>