Detailed Description

lb ≤ .5 xᵀQx + bᵀx ≤ ub Without loss of generality, the class stores a symmetric matrix Q.

For a non-symmetric matrix Q₀, we can define Q = (Q₀ + Q₀ᵀ) / 2, since xᵀQ₀x = xᵀQ₀ᵀx = xᵀ*(Q₀+Q₀ᵀ)/2 *x. The first equality holds because the transpose of a scalar is the scalar itself. Hence we can always convert a non-symmetric matrix Q₀ to a symmetric matrix Q.

#include <drake/solvers/constraint.h>

Public Types
enum	HessianType { kPositiveSemidefinite, kNegativeSemidefinite, kIndefinite, kZero }
	Whether the Hessian matrix is positive semidefinite, negative semidefinite, indefinite or a zero-matrix. More...

Public Member Functions
template<typename DerivedQ , typename Derivedb >
	QuadraticConstraint (const Eigen::MatrixBase< DerivedQ > &Q0, const Eigen::MatrixBase< Derivedb > &b, double lb, double ub, std::optional< HessianType > hessian_type=std::nullopt)
	Construct a quadratic constraint. More...

	~QuadraticConstraint () override

virtual const Eigen::MatrixXd &	Q () const
	The symmetric matrix Q, being the Hessian of this constraint. More...

virtual const Eigen::VectorXd &	b () const

HessianType	hessian_type () const

bool	is_convex () const
	Returns if this quadratic constraint is convex. More...

template<typename DerivedQ , typename DerivedB >
void	UpdateCoefficients (const Eigen::MatrixBase< DerivedQ > &new_Q, const Eigen::MatrixBase< DerivedB > &new_b, std::optional< HessianType > hessian_type=std::nullopt)
	Updates the quadratic and linear term of the constraint. More...

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

QuadraticConstraint &	operator= (const QuadraticConstraint &)=delete

	QuadraticConstraint (QuadraticConstraint &&)=delete

QuadraticConstraint &	operator= (QuadraticConstraint &&)=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

Static Public Attributes
static const int	kNumConstraints = 1

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)

Member Enumeration Documentation

◆ HessianType

enum HessianType

strong

Whether the Hessian matrix is positive semidefinite, negative semidefinite, indefinite or a zero-matrix.

Enumerator
kPositiveSemidefinite
kNegativeSemidefinite
kIndefinite
kZero

Constructor & Destructor Documentation

◆ QuadraticConstraint() [1/3]

QuadraticConstraint ( const QuadraticConstraint & )

delete

◆ QuadraticConstraint() [2/3]

QuadraticConstraint ( QuadraticConstraint && )

delete

◆ QuadraticConstraint() [3/3]

QuadraticConstraint	(	const Eigen::MatrixBase< DerivedQ > &	Q0,
		const Eigen::MatrixBase< Derivedb > &	b,
		double	lb,
		double	ub,
		std::optional< HessianType >	hessian_type = `std::nullopt`
	)

Construct a quadratic constraint.

Template Parameters

DerivedQ	The type for Q.
Derivedb	The type for b.

Parameters

Q0	The square matrix. Notice that Q₀ does not have to be symmetric.
b	The linear coefficient.
lb	The lower bound.
ub	The upper bound.
hessian_type	(optional) Indicates the type of Hessian matrix Q0. If hessian_type is not std::nullopt, then the user guarantees the type of Q0. If hessian_type=std::nullopt, then QuadraticConstraint will check the type of Q0. To speed up the constructor, set hessian_type != std::nullopt if you can. If this type is set incorrectly, then the downstream code (for example the solver) will malfunction.

Exceptions

std::exception if Q0 isn't a square matrix, or b.rows() != Q0.rows().

◆ ~QuadraticConstraint()

~QuadraticConstraint ( )

override

Member Function Documentation

◆ b()

virtual const Eigen::VectorXd& b ( ) const

virtual

◆ hessian_type()

HessianType hessian_type ( ) const

◆ is_convex()

bool is_convex ( ) const

Returns if this quadratic constraint is convex.

◆ operator=() [1/2]

QuadraticConstraint& operator= ( const QuadraticConstraint & )

delete

◆ operator=() [2/2]

QuadraticConstraint& operator= ( QuadraticConstraint && )

delete

◆ Q()

virtual const Eigen::MatrixXd& Q ( ) const

virtual

The symmetric matrix Q, being the Hessian of this constraint.

◆ UpdateCoefficients()

void UpdateCoefficients	(	const Eigen::MatrixBase< DerivedQ > &	new_Q,
		const Eigen::MatrixBase< DerivedB > &	new_b,
		std::optional< HessianType >	hessian_type = `std::nullopt`
	)

Updates the quadratic and linear term of the constraint.

The new matrices need to have the same dimension as before.

Parameters

new_Q	new quadratic term
new_b	new linear term
hessian_type	(optional) Indicates the type of Hessian matrix Q0. If hessian_type is not std::nullopt, then the user guarantees the type of Q0. If hessian_type=std::nullopt, then QuadraticConstraint will check the type of Q0. To speed up the constructor, set hessian_type != std::nullopt if you can.

Member Data Documentation

◆ kNumConstraints

const int kNumConstraints = 1

static

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

drake/solvers/constraint.h

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ HessianType

Constructor & Destructor Documentation

◆ QuadraticConstraint() [1/3]

◆ QuadraticConstraint() [2/3]

◆ QuadraticConstraint() [3/3]

◆ ~QuadraticConstraint()

Member Function Documentation

◆ b()

◆ hessian_type()

◆ is_convex()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ Q()

◆ UpdateCoefficients()

Member Data Documentation

◆ kNumConstraints