A wrapper of the ql algorithm by Professor Schittkowski, with some convention changes on the way the constraints are written. More...

#include <eigen-qld/QLD.h>

Inheritance diagram for Eigen::QLD:

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Collaboration diagram for Eigen::QLD:

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Public Member Functions
EIGEN_QLD_API	QLD ()

EIGEN_QLD_API	QLD (int nrvar, int nreq, int nrineq, int ldq=-1, bool verbose=false)

EIGEN_QLD_API void	problem (int nrvar, int nreq, int nrineq, int ldq=-1)

EIGEN_QLD_API const VectorXd &	multipliers () const

template<typename MatObj , typename VecObj , typename MatEq , typename VecEq , typename MatIneq , typename VecIneq , typename VecVar >
bool	solve (const MatrixBase< MatObj > &Q, const MatrixBase< VecObj > &c, const MatrixBase< MatEq > &Aeq, const MatrixBase< VecEq > &beq, const MatrixBase< MatIneq > &Aineq, const MatrixBase< VecIneq > &bineq, const MatrixBase< VecVar > &xl, const MatrixBase< VecVar > &xu, bool isDecomp=false, double eps=1e-12)

Public Member Functions inherited from Eigen::QLDDirect
EIGEN_QLD_API	QLDDirect ()

EIGEN_QLD_API	QLDDirect (int nrvar, int nreq, int nrineq, int ldq=-1, int lda=-1, bool verbose=false)

EIGEN_QLD_API void	fdOut (int fd)

EIGEN_QLD_API int	fdOut () const

EIGEN_QLD_API void	verbose (bool v)

EIGEN_QLD_API bool	verbose () const

EIGEN_QLD_API int	fail () const

EIGEN_QLD_API void	problem (int nrvar, int nreq, int nrineq, int ldq=-1, int lda=-1)

EIGEN_QLD_API const VectorXd &	result () const

EIGEN_QLD_API const VectorXd &	multipliers () const

template<typename MatObj , typename VecObj , typename MatConstr , typename VecConstr , typename VecVar >
bool	solve (const MatrixBase< MatObj > &Q, const MatrixBase< VecObj > &c, const MatrixBase< MatConstr > &A, const MatrixBase< VecConstr > &b, const MatrixBase< VecVar > &xl, const MatrixBase< VecVar > &xu, int nreq, bool isDecomp=false, double eps=1e-12)

Detailed Description

A wrapper of the ql algorithm by Professor Schittkowski, with some convention changes on the way the constraints are written.

Constructor & Destructor Documentation

◆ QLD() [1/2]

EIGEN_QLD_API Eigen::QLD::QLD ( )

Create a solver without allocating memory. A call to QLD::problem will be necessary before calling QLD::solve

◆ QLD() [2/2]

EIGEN_QLD_API Eigen::QLD::QLD	(	int	nrvar,
		int	nreq,
		int	nrineq,
		int	ldq = `-1`,
		bool	verbose = `false`
	)

Create a solver and allocate the memory necessary to solve a problem with the given dimensions. See also QLD::problem

Member Function Documentation

◆ multipliers()

EIGEN_QLD_API const VectorXd& Eigen::QLD::multipliers ( ) const

Return the lagrange multipliers associated with results, with the multipliers corresponding to equality constraints first, then to inequality constraints, then lower bounds, then upper bounds.

Warning: These are the lagrange multipliers as computed by the underlying ql solver, for which the constraints have the form \( A_{eq} + b_{eq} = 0\) and \( A_{ineq} + b_{ineq} >= 0\).
For now, QLD::solve is changing automatically the constraints, but not the multipliers. After a call to QLD::solveNoOverhead, the multipliers have the same meaning as for ql.

◆ problem()

EIGEN_QLD_API void Eigen::QLD::problem	(	int	nrvar,
		int	nreq,
		int	nrineq,
		int	ldq = `-1`
	)

Allocate the memory necessary to solve a problem with the given dimensions.

Parameters

nrvar	Size of the variable vector \(x\).
nreq	Number of equality constraints, i.e. the row size of \(A_{eq}\).
nrineq	Number of inequality constraints, i.e. the row size of \(A_{ineq}\).
ldq	Leading dimension of the matrix \(Q\) (see QLDDirect::problem). If smaller than `nrvar`, `nrvar` will be used instead (which is the default case).

◆ solve()

template<typename MatObj , typename VecObj , typename MatEq , typename VecEq , typename MatIneq , typename VecIneq , typename VecVar >

bool Eigen::QLD::solve	(	const MatrixBase< MatObj > &	Q,
		const MatrixBase< VecObj > &	c,
		const MatrixBase< MatEq > &	Aeq,
		const MatrixBase< VecEq > &	beq,
		const MatrixBase< MatIneq > &	Aineq,
		const MatrixBase< VecIneq > &	bineq,
		const MatrixBase< VecVar > &	xl,
		const MatrixBase< VecVar > &	xu,
		bool	isDecomp = `false`,
		double	eps = `1e-12`
	)

inline

Solve the problem

\begin{align} \underset{{x} \in \mathbb{R}^n}{\text{minimize}} & \ \frac{1}{2}{x^TQx} + {c^Tx} \nonumber \\ \text{subject to} & \ A_{eq} x = b_{eq} \\ & \ A_{ineq} x \leq b_{ineq} \\ & \ x_l \leq x \leq x_u \end{align}

For a positive definite matrix \(Q\), we have the Cholesky decomposition \(Q = R^T R\) with \(R\) upper triangular. If isDecomp is true, \(R\) should be given instead of \(Q\). Only the upper triangular part of \(R\) will be used.