Functions
double	solve_quadprog (const Eigen::MatrixXd &_G, const Eigen::VectorXd &g0, const Eigen::MatrixXd &_CE, const Eigen::VectorXd &ce0, const Eigen::MatrixXd &_CI, const Eigen::VectorXd &ci0, Eigen::VectorXd &x)

void	compute_d (Eigen::VectorXd &d, const Eigen::MatrixXd &J, const Eigen::VectorXd &np)

void	update_z (Eigen::VectorXd &z, const Eigen::MatrixXd &J, const Eigen::VectorXd &d, int iq)

void	update_r (const Eigen::MatrixXd &R, Eigen::VectorXd &r, const Eigen::VectorXd &d, int iq)

bool	add_constraint (Eigen::MatrixXd &R, Eigen::MatrixXd &J, Eigen::VectorXd &d, int &iq, double &rnorm)

void	delete_constraint (Eigen::MatrixXd &R, Eigen::MatrixXd &J, Eigen::VectorXi &A, Eigen::VectorXd &u, int n, int p, int &iq, int l)

void	cholesky_decomposition (Eigen::MatrixXd &A)

void	cholesky_solve (const Eigen::MatrixXd &L, Eigen::VectorXd &x, const Eigen::VectorXd &b)

void	forward_elimination (const Eigen::MatrixXd &L, Eigen::VectorXd &y, const Eigen::VectorXd &b)

void	backward_elimination (const Eigen::MatrixXd &U, Eigen::VectorXd &x, const Eigen::VectorXd &y)

double	scalar_product (const Eigen::VectorXd &x, const Eigen::VectorXd &y)

double	distance (double a, double b)

void	print_matrix (const char *name, const Eigen::MatrixXd &A, int n=-1, int m=-1)

template<typename T >
void	print_vector (const char *name, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, int n=-1)

Function Documentation

bool QuadProgPP::add_constraint	(	Eigen::MatrixXd &	R,
		Eigen::MatrixXd &	J,
		Eigen::VectorXd &	d,
		int &	iq,
		double &	rnorm
	)

Definition at line 566 of file QuadProg++.cpp.

void QuadProgPP::backward_elimination	(	const Eigen::MatrixXd &	U,
		Eigen::VectorXd &	x,
		const Eigen::VectorXd &	y
	)

inline

Definition at line 804 of file QuadProg++.cpp.

void QuadProgPP::cholesky_decomposition ( Eigen::MatrixXd & A )

Definition at line 745 of file QuadProg++.cpp.

void QuadProgPP::cholesky_solve	(	const Eigen::MatrixXd &	L,
		Eigen::VectorXd &	x,
		const Eigen::VectorXd &	b
	)

Definition at line 778 of file QuadProg++.cpp.

void QuadProgPP::compute_d	(	Eigen::VectorXd &	d,
		const Eigen::MatrixXd &	J,
		const Eigen::VectorXd &	np
	)

inline

Definition at line 523 of file QuadProg++.cpp.

void QuadProgPP::delete_constraint	(	Eigen::MatrixXd &	R,
		Eigen::MatrixXd &	J,
		Eigen::VectorXi &	A,
		Eigen::VectorXd &	u,
		int	n,
		int	p,
		int &	iq,
		int	l
	)

Definition at line 637 of file QuadProg++.cpp.

double QuadProgPP::distance	(	double	a,
		double	b
	)

inline

Definition at line 714 of file QuadProg++.cpp.

void QuadProgPP::forward_elimination	(	const Eigen::MatrixXd &	L,
		Eigen::VectorXd &	y,
		const Eigen::VectorXd &	b
	)

inline

Definition at line 790 of file QuadProg++.cpp.

void QuadProgPP::print_matrix	(	const char *	name,
		const Eigen::MatrixXd &	A,
		int	n = `-1`,
		int	m = `-1`
	)

Definition at line 818 of file QuadProg++.cpp.

template<typename T >

void QuadProgPP::print_vector	(	const char *	name,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	v,
		int	n = `-1`
	)

Definition at line 842 of file QuadProg++.cpp.

double QuadProgPP::scalar_product	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	y
	)

inline

Definition at line 734 of file QuadProg++.cpp.

double QuadProgPP::solve_quadprog	(	const Eigen::MatrixXd &	_G,
		const Eigen::VectorXd &	g0,
		const Eigen::MatrixXd &	_CE,
		const Eigen::VectorXd &	ce0,
		const Eigen::MatrixXd &	_CI,
		const Eigen::VectorXd &	ci0,
		Eigen::VectorXd &	x
	)

The quadprog_solve() function implements the algorithm of Goldfarb and Idnani for the solution of a (convex) Quadratic Programming problem by means of an active-set dual method.

The quadratic problem with $n$ variables and $m$ constraints is:

$\begin{align*} \argmin{\x} &: \; \frac{1}{2} \x\tp G \x + \vec{g}_0\tp \x \\ & CE\tp \x + \vec{ce}_0 = \vec{0} \\ & CI\tp \x + \vec{ci}_0 \geq \vec{0} \end{align*}$

The matrix and vectors dimensions are as follows:

$G$ : $n \times n$

$\vec{g}_0$ : $n$

$CE$ : $n \times p$

$\vec{ce}_0$ : $p$

$CI$ : $n \times m$

$\vec{ci}_0$ : $m$

$x$ : $n$

The function will return the cost of the solution written in the $x$ vector or std::numeric_limits::infinity() if the problem is infeasible. In the latter case the value of the $x$ vector is not correct.

Parameters

_G	n x n Symmetric positive definite matrix.
g0	Vector of size n, where n is the number of variables.
_CE	Matrix of size n x p, where p is the number of equalities.
ce0	Vector of size p.
_CI	Matrix of size n x m, where m is the number of inequalities.
ci0	Vector of size m.
x	Problem variables of size n.

Note: Pay attention in setting up the vectors $\vec{ce}_0$ and $\vec{ci}_0$ . If the constraints of your problem are specified in the form and $C^T x \geq d$ , then you should set $\vec{ce}_0 = -b$ and $\vec{ci}_0 = -d$ . Also the matrix is modified within the function since it is used to compute the cholesky factorization for further computations inside the function. If you need the original matrix you should make a copy of it and pass the copy to the function. [goldfarb1983numerically]

Returns: cost of the solution written in the x vector or std::numeric_limits::infinity() if the problem is infeasible. In the latter case the value of the vector is not correct.

Author: Luca Di Gaspero, DIEGM - University of Udine, Italy.

Copyright: GNU Lesser General Public License.; 2007-2009 Luca Di Gaspero.; 2007-2009 Luca Di Gaspero.

Definition at line 75 of file QuadProg++.cpp.

void QuadProgPP::update_r	(	const Eigen::MatrixXd &	R,
		Eigen::VectorXd &	r,
		const Eigen::VectorXd &	d,
		int	iq
	)

inline

Definition at line 551 of file QuadProg++.cpp.

void QuadProgPP::update_z	(	Eigen::VectorXd &	z,
		const Eigen::MatrixXd &	J,
		const Eigen::VectorXd &	d,
		int	iq
	)

inline

Definition at line 538 of file QuadProg++.cpp.

Functions

Function Documentation