Drake
LorentzConeConstraint Class Reference

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

#include <drake/solvers/constraint.h>

Inheritance diagram for LorentzConeConstraint:
Collaboration diagram for LorentzConeConstraint:

Public Member Functions

 LorentzConeConstraint (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)
 
 ~LorentzConeConstraint () override
 
const Eigen::MatrixXd & A () 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
 Constraint (const Constraint &)=delete
 
Constraintoperator= (const Constraint &)=delete
 
 Constraint (Constraint &&)=delete
 
Constraintoperator= (Constraint &&)=delete
 
- Public Member Functions inherited from EvaluatorBase
template<typename DerivedLB , typename DerivedUB >
 EvaluatorBase (size_t num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub)
 
template<typename DerivedLB , typename DerivedUB >
 EvaluatorBase (size_t num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub, const std::string &description)
 
virtual ~EvaluatorBase ()
 
void Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd &y) const
 
void Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd &y) const
 
bool CheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, const 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, const double tol=1E-6) const
 
Eigen::VectorXd const & lower_bound () const
 
Eigen::VectorXd const & upper_bound () const
 
size_t num_constraints () const
 
template<typename Derived >
void UpdateLowerBound (const Eigen::MatrixBase< Derived > &new_lb)
 
template<typename Derived >
void UpdateUpperBound (const Eigen::MatrixBase< Derived > &new_ub)
 
void set_description (const std::string &description)
 
const std::string & get_description () const
 
template<typename DerivedL , typename DerivedU >
void set_bounds (const Eigen::MatrixBase< DerivedL > &lower_bound, const Eigen::MatrixBase< DerivedU > &upper_bound)
 Set the upper and lower bounds of the constraint. More...
 
int num_vars () const
 Getter for the number of variables in the constraint, namely the number of rows in x, as used in Eval(x, y). More...
 
 EvaluatorBase (const EvaluatorBase &)=delete
 
EvaluatorBaseoperator= (const EvaluatorBase &)=delete
 
 EvaluatorBase (EvaluatorBase &&)=delete
 
EvaluatorBaseoperator= (EvaluatorBase &&)=delete
 

Protected Member Functions

void DoEval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd &y) const override
 
void DoEval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd &y) const override
 
- Protected Member Functions inherited from EvaluatorBase
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
 
 EvaluatorBase (size_t num_constraints, int num_vars)
 Constructs a constraint which has num_constraints rows, with input variables to Eval a num_vars x 1 vector. More...
 

Detailed Description

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

A vector \( z \in \mathbb{R}^n \) lies within Lorentz cone if

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

where \( A\in\mathbb{R}^{n\times m}, b\in\mathbb{R}^{n}\) 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 \( b \).

For more information and visualization, please refer to https://inst.eecs.berkeley.edu/~ee127a/book/login/l_socp_soc.html

Constructor & Destructor Documentation

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

Member Function Documentation

const Eigen::MatrixXd& A ( ) const
inline

Getter for A.

const Eigen::VectorXd& b ( ) const
inline

Getter for b.

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

Implements EvaluatorBase.

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

Implements EvaluatorBase.

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LorentzConeConstraint& operator= ( LorentzConeConstraint &&  )
delete
LorentzConeConstraint& operator= ( const LorentzConeConstraint )
delete

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