CGAL::Quadratic_program_from_mps<NT>

#include <CGAL/QP_models.h>

Definition

(QP)$$	minimize$$	xTDx+cTx+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 $$l_j {- } for all $$j
• $$u is an $$n-dimensional vector of upper bounds for $$x, where $$u_j { } 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

Types

Creation

Operations

bool	qp.is_valid ()	returns true if and only if an MPS-encoded quadratic program could be extracted from the input stream.
std::string	qp.get_error ()	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)
		returns the name of the $$j-th variable. Precondition:  j must not refer to a variable that has been added later, using one of the set methods below.
int	qp.variable_index_by_name ( std::string name)
		returns the index of the variable with name name. If there is no variable with this name, the result is $$-1.
std::string	qp.constraint_name_by_index ( int i)
		returns the name of the $$i-th constraint. Precondition:  i must not refer to a constraint that has been added later, using one of the set methods below.
int	qp.constraint_index_by_name ( std::string name)
		returns the index of the constraint with name name. If there is no constraint with this name, the result is $$-1.
bool	qp.is_linear ()	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_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

See Also