Drake
ExponentialConeConstraint Class Reference

## 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

ExponentialConeConstraintoperator= (const ExponentialConeConstraint &)=delete

ExponentialConeConstraint (ExponentialConeConstraint &&)=delete

ExponentialConeConstraintoperator= (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

Constraintoperator= (const Constraint &)=delete

Constraint (Constraint &&)=delete

Constraintoperator= (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...

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...

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...

EvaluatorBase (const EvaluatorBase &)=delete

EvaluatorBaseoperator= (const EvaluatorBase &)=delete

EvaluatorBase (EvaluatorBase &&)=delete

EvaluatorBaseoperator= (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... Protected Member Functions inherited from Constraint
void UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)

void UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)

void set_bounds (const Eigen::Ref< const Eigen::VectorXd > &lower_bound, const Eigen::Ref< const Eigen::VectorXd > &upper_bound)
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)

## ◆ 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

## ◆ A()

 const Eigen::SparseMatrix& 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

## ◆ operator=() [1/2]

 ExponentialConeConstraint& operator= ( const ExponentialConeConstraint & )
delete

## ◆ operator=() [2/2]

 ExponentialConeConstraint& operator= ( ExponentialConeConstraint && )
delete

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