Quadratic_program<NT>

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CGAL::Quadratic_program<NT>

Definition

An object of class Quadratic_program<NT> describes a convex quadratic program of the form

(QP)	minimize	x^TDx+c^Tx+c₀
	subject to	Ax ⋛ b,
		l ≤ x ≤ u

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 { ≤ , =, ≥ },
l is an n-dimensional vector of lower bounds for x, where l_j ∈ ℝ ∪ {-∞} for all j
u is an n-dimensional vector of upper bounds for x, where u_j ∈ ℝ ∪ {∞} for all j
D is a symmetric positive-semidefinite n × n matrix (the quadratic objective function),
c is an n-dimensional vector (the linear objective function), and
c₀ is a constant.

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 () const

returns true if and only if qp is a linear program.

bool

qp.is_nonnegative () const

returns true if and only if qp is a nonnegative program.

void

qp.set_a ( int j, int i, NT val)

sets the entry A_ij 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 b_i 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 l_j of qp to val, otherwise it sets l_j 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 u_j of qp to val, otherwise it sets u_j 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 c_j 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 2D_ij and 2D_ji 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

CGAL::Quadratic_program<NT>

Definition

Is Model for the Concepts

Types

Creation

Operations

Example

See Also