Drake
LorentzConeConstraint Class Reference

Constraining the linear expression $$z=Ax+b$$ lies within the Lorentz cone. More...

#include <drake/solvers/constraint.h>

## Public Member Functions

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

~LorentzConeConstraint () override

const Eigen::MatrixXdA () const
Getter for A. More...

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

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

LorentzConeConstraintoperator= (const LorentzConeConstraint &)=delete

LorentzConeConstraint (LorentzConeConstraint &&)=delete

LorentzConeConstraintoperator= (LorentzConeConstraint &&)=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...

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...

EvaluatorBase (const EvaluatorBase &)=delete

EvaluatorBaseoperator= (const EvaluatorBase &)=delete

EvaluatorBase (EvaluatorBase &&)=delete

EvaluatorBaseoperator= (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 > &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...

void set_num_outputs (int num_outputs)

## Detailed Description

Constraining the linear expression $$z=Ax+b$$ lies within the Lorentz cone.

A vector z ∈ ℝ ⁿ lies within Lorentz cone if

$z_0 \ge \sqrt{z_1^2+...+z_{n-1}^2}$

where A ∈ ℝ ⁿˣᵐ, b ∈ ℝ ⁿ are given matrices. Ideally this constraint should be handled by a second-order cone solver. In case the user wants to enforce this constraint through general nonlinear optimization, with smooth gradient, we alternatively impose the following constraint, with smooth gradient everywhere

$a_0^Tx+b_0\ge 0\\ (a_0^Tx+b_0)^2-(a_1^Tx+b_1)^2-...-(a_{n-1}^Tx+b_{n-1})^2 \ge 0$

where $$a_i^T$$ is the i'th row of matrix $$A$$. $$b_i$$ is the i'th entry of vector $$b$$.

## ◆ LorentzConeConstraint() [1/3]

 LorentzConeConstraint ( const LorentzConeConstraint & )
delete

## ◆ LorentzConeConstraint() [2/3]

 LorentzConeConstraint ( LorentzConeConstraint && )
delete

## ◆ LorentzConeConstraint() [3/3]

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

## ◆ ~LorentzConeConstraint()

 ~LorentzConeConstraint ( )
override

## ◆ A()

 const Eigen::MatrixXd& A ( ) const

Getter for A.

## ◆ b()

 const Eigen::VectorXd& b ( ) const

Getter for b.

## ◆ operator=() [1/2]

 LorentzConeConstraint& operator= ( const LorentzConeConstraint & )
delete

## ◆ operator=() [2/2]

 LorentzConeConstraint& operator= ( LorentzConeConstraint && )
delete

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