Detailed Description

Constraining that the linear expression \( z=Ax+b \) lies within rotated Lorentz cone.

A vector z ∈ ℝ ⁿ lies within rotated Lorentz cone, if

\[ z_0 \ge 0\\ z_1 \ge 0\\ z_0 z_1 \ge z_2^2 + z_3^2 + ... + z_{n-1}^2 \]

where A ∈ ℝ ⁿˣᵐ, b ∈ ℝ ⁿ are given matrices.

For more information and visualization, please refer to https://docs.mosek.com/modeling-cookbook/cqo.html (Fig 3.1)

#include <drake/solvers/constraint.h>

Public Member Functions
	RotatedLorentzConeConstraint (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)

const Eigen::SparseMatrix< double > &	A () const
	Getter for A. More...

const Eigen::MatrixXd &	A_dense () const
	Getter for dense version of A. More...

const Eigen::VectorXd &	b () const
	Getter for b. More...

	~RotatedLorentzConeConstraint () override

void	UpdateCoefficients (const Eigen::Ref< const Eigen::MatrixXd > &new_A, const Eigen::Ref< const Eigen::VectorXd > &new_b)
	Updates the coefficients, the updated constraint is z=new_A * x + new_b in the rotated Lorentz cone. More...

Does not allow copy, move, or assignment
	RotatedLorentzConeConstraint (const RotatedLorentzConeConstraint &)=delete

RotatedLorentzConeConstraint &	operator= (const RotatedLorentzConeConstraint &)=delete

	RotatedLorentzConeConstraint (RotatedLorentzConeConstraint &&)=delete

RotatedLorentzConeConstraint &	operator= (RotatedLorentzConeConstraint &&)=delete

Public Member Functions inherited from Constraint
template<typename DerivedLB , typename DerivedUB >
	Constraint (int num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub, const std::string &description="")
	Constructs a constraint which has `num_constraints` rows, with an input `num_vars` x 1 vector. More...

	Constraint (int num_constraints, int num_vars)
	Constructs a constraint which has `num_constraints` rows, with an input `num_vars` x 1 vector, with no bounds. More...

bool	CheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=1E-6) const
	Return whether this constraint is satisfied by the given value, `x`. More...

bool	CheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, double tol=1E-6) const

symbolic::Formula	CheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const

const Eigen::VectorXd &	lower_bound () const

const Eigen::VectorXd &	upper_bound () const

int	num_constraints () const
	Number of rows in the output constraint. More...

	Constraint (const Constraint &)=delete

Constraint &	operator= (const Constraint &)=delete

	Constraint (Constraint &&)=delete

Constraint &	operator= (Constraint &&)=delete

Public Member Functions inherited from EvaluatorBase
virtual	~EvaluatorBase ()

void	Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const
	Evaluates the expression. More...

void	Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const
	Evaluates the expression. More...

void	Eval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const
	Evaluates the expression. More...

void	set_description (const std::string &description)
	Set a human-friendly description for the evaluator. More...

const std::string &	get_description () const
	Getter for a human-friendly description for the evaluator. More...

std::ostream &	Display (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	Formats this evaluator into the given stream using `vars` for the bound decision variable names. More...

std::ostream &	Display (std::ostream &os) const
	Formats this evaluator into the given stream, without displaying the decision variables it is bound to. More...

std::string	ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const
	Returns a LaTeX string describing this evaluator. More...

int	num_vars () const
	Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y). More...

int	num_outputs () const
	Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y). More...

void	SetGradientSparsityPattern (const std::vector< std::pair< int, int >> &gradient_sparsity_pattern)
	Set the sparsity pattern of the gradient matrix ∂y/∂x (the gradient of y value in Eval, w.r.t x in Eval) . More...

const std::optional< std::vector< std::pair< int, int > > > &	gradient_sparsity_pattern () const
	Returns the vector of (row_index, col_index) that contains all the entries in the gradient of Eval function (∂y/∂x) whose value could be non-zero, namely if ∂yᵢ/∂xⱼ could be non-zero, then the pair (i, j) is in gradient_sparsity_pattern. More...

bool	is_thread_safe () const
	Returns whether it is safe to call Eval in parallel. More...

	EvaluatorBase (const EvaluatorBase &)=delete

EvaluatorBase &	operator= (const EvaluatorBase &)=delete

	EvaluatorBase (EvaluatorBase &&)=delete

EvaluatorBase &	operator= (EvaluatorBase &&)=delete

Additional Inherited Members
Protected Member Functions inherited from Constraint
void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound. More...

void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound. More...

void	set_bounds (const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Set the upper and lower bounds of the constraint. More...

virtual bool	DoCheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, const double tol) const

virtual bool	DoCheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, const double tol) const

virtual symbolic::Formula	DoCheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const

Protected Member Functions inherited from EvaluatorBase
	EvaluatorBase (int num_outputs, int num_vars, const std::string &description="")
	Constructs a evaluator. More...

void	set_num_outputs (int num_outputs)

void	set_is_thread_safe (bool is_thread_safe)

Constructor & Destructor Documentation

◆ RotatedLorentzConeConstraint() [1/3]

RotatedLorentzConeConstraint ( const RotatedLorentzConeConstraint & )

delete

◆ RotatedLorentzConeConstraint() [2/3]

RotatedLorentzConeConstraint ( RotatedLorentzConeConstraint && )

delete

◆ RotatedLorentzConeConstraint() [3/3]

RotatedLorentzConeConstraint	(	const Eigen::Ref< const Eigen::MatrixXd > &	A,
		const Eigen::Ref< const Eigen::VectorXd > &	b
	)

Exceptions

std::exception if A.rows() < 3.

◆ ~RotatedLorentzConeConstraint()

~RotatedLorentzConeConstraint ( )

override

Member Function Documentation

◆ A()

const Eigen::SparseMatrix<double>& A ( ) const

Getter for A.

◆ A_dense()

const Eigen::MatrixXd& A_dense ( ) const

Getter for dense version of A.

◆ b()

const Eigen::VectorXd& b ( ) const

Getter for b.

◆ operator=() [1/2]

RotatedLorentzConeConstraint& operator= ( RotatedLorentzConeConstraint && )

delete

◆ operator=() [2/2]

RotatedLorentzConeConstraint& operator= ( const RotatedLorentzConeConstraint & )

delete

◆ UpdateCoefficients()

void UpdateCoefficients	(	const Eigen::Ref< const Eigen::MatrixXd > &	new_A,
		const Eigen::Ref< const Eigen::VectorXd > &	new_b
	)

Updates the coefficients, the updated constraint is z=new_A * x + new_b in the rotated Lorentz cone.

Exceptions

std::exception if the new_A.cols() != A.cols(), namely the variable size should not change.

Precondition: new_A.rows() >= 3 and new_A.rows() == new_b.rows().

The documentation for this class was generated from the following file:

drake/solvers/constraint.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ RotatedLorentzConeConstraint() [1/3]

◆ RotatedLorentzConeConstraint() [2/3]

◆ RotatedLorentzConeConstraint() [3/3]

◆ ~RotatedLorentzConeConstraint()

Member Function Documentation

◆ A()

◆ A_dense()

◆ b()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ UpdateCoefficients()