Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C

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CGAL::Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>

Definition

An object of class Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it> 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.

This class is simply a wrapper for existing iterators, and it does not copy the program data.

It frequently happens that all values in one of the vectors from above are the same, for example if the system Ax ⋛ b is actually a system of equations Ax=b. To get an iterator over such a vector, it is not necessary to store multiple copies of the value in some container; an instance of the class Const_oneset_iterator<T>, constructed from the value in question, does the job more efficiently.

Is Model for the Concepts

QuadraticProgram

Creation

Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it> qp ( int n,
int m,
A_it a,
B_it b,
R_it r,
FL_it fl,
L_it l,
FU_it fu,
U_it u,
D_it d,
C_it c,
std::iterator_traits<C_it>value_type c0 = 0);

constructs qp from given random-access iterators and the constant c0. The passed iterators are merely stored, no copying of the program data takes place. How these iterators are supposed to encode the quadratic program is described in QuadraticProgram.

Example

QP_solver/first_qp_from_iterators.cpp

The following example for the simpler model Nonnegative_linear_program_from_iterators<A_it, B_it, R_it, C_it> should give you a flavor of the use of this model in practice.

QP_solver/solve_convex_hull_containment_lp.h
QP_solver/convex_hull_containment.cpp

CGAL::Quadratic_program_from_iterators<A_it, B_it, R_it, FL_it, L_it, FU_it, U_it, D_it, C_it>

Definition

Is Model for the Concepts

Creation

Example

See Also