Detailed Description

An exponential cone constraint is a special type of convex cone constraint.

We constrain A * x + b to be in the exponential cone, where A has 3 rows, and b is in ℝ³, x is the decision variable. A vector z in ℝ³ is in the exponential cone, if {z₀, z₁, z₂ | z₀ ≥ z₁ * exp(z₂ / z₁), z₁ > 0}. Equivalently, this constraint can be refomulated with logarithm function {z₀, z₁, z₂ | z₂ ≤ z₁ * log(z₀ / z₁), z₀ > 0, z₁ > 0}

The Eval function implemented in this class is z₀ - z₁ * exp(z₂ / z₁) >= 0, z₁ > 0 where z = A * x + b. It is not recommended to solve an exponential cone constraint through generic nonlinear optimization. It is possible that the nonlinear solver can accidentally set z₁ = 0, where the constraint is not well defined. Instead, the user should consider to solve the program through conic solvers that can exploit exponential cone, such as MOSEK™ and SCS.

#include <drake/solvers/constraint.h>

Public Member Functions
	ExponentialConeConstraint (const Eigen::Ref< const Eigen::SparseMatrix< double >> &A, const Eigen::Ref< const Eigen::Vector3d > &b)
	Constructor for exponential cone. More...

	~ExponentialConeConstraint () override

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

const Eigen::Vector3d &	b () const
	Getter for vector b. More...

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

ExponentialConeConstraint &	operator= (const ExponentialConeConstraint &)=delete

	ExponentialConeConstraint (ExponentialConeConstraint &&)=delete

ExponentialConeConstraint &	operator= (ExponentialConeConstraint &&)=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

Protected Member Functions
template<typename DerivedX , typename ScalarY >
void	DoEvalGeneric (const Eigen::MatrixBase< DerivedX > &x, VectorX< ScalarY > *y) const

void	DoEval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const override
	Implements expression evaluation for scalar type double. More...

void	DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const override
	Implements expression evaluation for scalar type AutoDiffXd. More...

void	DoEval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const override
	Implements expression evaluation for scalar type symbolic::Expression. More...

std::string	DoToLatex (const VectorX< symbolic::Variable > &, int) const override

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...

virtual std::ostream &	DoDisplay (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	NVI implementation of Display. More...

void	set_num_outputs (int num_outputs)

void	set_is_thread_safe (bool is_thread_safe)

Constructor & Destructor Documentation

◆ ExponentialConeConstraint() [1/3]

ExponentialConeConstraint ( const ExponentialConeConstraint & )

delete

◆ ExponentialConeConstraint() [2/3]

ExponentialConeConstraint ( ExponentialConeConstraint && )

delete

◆ ExponentialConeConstraint() [3/3]

ExponentialConeConstraint	(	const Eigen::Ref< const Eigen::SparseMatrix< double >> &	A,
		const Eigen::Ref< const Eigen::Vector3d > &	b
	)

Constructor for exponential cone.

Constrains A * x + b to be in the exponential cone.

Precondition: A has 3 rows.

◆ ~ExponentialConeConstraint()

~ExponentialConeConstraint ( )

override

Member Function Documentation

◆ A()

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

Getter for matrix A.

◆ b()

const Eigen::Vector3d& b ( ) const

Getter for vector b.

◆ DoEval() [1/3]

void DoEval	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		Eigen::VectorXd *	y
	)		const

overrideprotectedvirtual

Implements expression evaluation for scalar type double.

Parameters

x	Input vector.
y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoEval() [2/3]

void DoEval	(	const Eigen::Ref< const AutoDiffVecXd > &	x,
		AutoDiffVecXd *	y
	)		const

overrideprotectedvirtual

Implements expression evaluation for scalar type AutoDiffXd.

Parameters

x	Input vector.
y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoEval() [3/3]

void DoEval	(	const Eigen::Ref< const VectorX< symbolic::Variable >> &	x,
		VectorX< symbolic::Expression > *	y
	)		const

overrideprotectedvirtual

Implements expression evaluation for scalar type symbolic::Expression.

Parameters

[in]	x	Input vector.
[out]	y	Output vector.

Precondition: x must be of size num_vars x 1.

Postcondition: y will be of size num_outputs x 1.

Implements EvaluatorBase.

◆ DoEvalGeneric()

void DoEvalGeneric	(	const Eigen::MatrixBase< DerivedX > &	x,
		VectorX< ScalarY > *	y
	)		const

protected

◆ DoToLatex()

std::string DoToLatex	(	const VectorX< symbolic::Variable > &	,
		int
	)		const

overrideprotectedvirtual

Reimplemented from EvaluatorBase.

◆ operator=() [1/2]

ExponentialConeConstraint& operator= ( ExponentialConeConstraint && )

delete

◆ operator=() [2/2]

ExponentialConeConstraint& operator= ( const ExponentialConeConstraint & )

delete

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

drake/solvers/constraint.h

Detailed Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ ExponentialConeConstraint() [1/3]

◆ ExponentialConeConstraint() [2/3]

◆ ExponentialConeConstraint() [3/3]

◆ ~ExponentialConeConstraint()

Member Function Documentation

◆ A()

◆ b()

◆ DoEval() [1/3]

◆ DoEval() [2/3]

◆ DoEval() [3/3]

◆ DoEvalGeneric()

◆ DoToLatex()

◆ operator=() [1/2]

◆ operator=() [2/2]