Quadratic_program_from

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CGAL::Quadratic_program_from_mps<NT>

Definition

An object of class Quadratic_program_from_mps<NT> describes a convex quadratic program of the general 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.

The program data are read from an input stream in MPSFormat. This is a commonly used format for encoding linear and quadratic programs that is understood by many solvers. All values are expected to be readable into type NT. The constructed program can be further manipulated by using the set-methods below.

Is Model for the Concepts

QuadraticProgram
LinearProgram
NonnegativeQuadraticProgram
NonnegativeLinearProgram

Types

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

Creation

Quadratic_program_from_mps<NT> qp ( std::istream& in);
	reads qp from the input stream in.

Operations

bool

qp.is_valid () const

returns true if and only if an MPS-encoded quadratic program could be extracted from the input stream.

std::string

qp.get_error () const

if !qp.is_valid(), this method returns an error message explaining why the input does not conform to the MPSFormat.

std::string

qp.variable_name_by_index ( int j) const

returns the name of the j-th variable.

Precondition:

j must not refer to a variable that has been added later, using one of the set methods below.

int

qp.variable_index_by_name ( std::string name) const

returns the index of the variable with name name. If there is no variable with this name, the result is -1.

std::string

qp.constraint_name_by_index ( int i) const

returns the name of the i-th constraint.

Precondition:

i must not refer to a constraint that has been added later, using one of the set methods below.

int

qp.constraint_index_by_name ( std::string name) const

returns the index of the constraint with name name. If there is no constraint with this name, the result is -1.

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_from_mps.cpp
QP_solver/first_lp_from_mps.cpp
QP_solver/first_nonnegative_qp_from_mps.cpp
QP_solver/first_nonnegative_lp_from_mps.cpp

CGAL::Quadratic_program_from_mps<NT>

Definition

Is Model for the Concepts

Types

Creation

Operations

Example

See Also