PerspectiveQuadraticCost Class Reference

Detailed Description

If \( z = Ax + b,\) implements a cost of the form:

\[ (z_1^2 + z_2^2 + ... + z_{n-1}^2) / z_0. \]

Note that this cost is convex when we additionally constrain z_0 > 0.

It is treated as a generic nonlinear objective by most solvers.

Costs of this form are sometimes referred to as "quadratic over linear".

#include <drake/solvers/cost.h>

Public Member Functions
	PerspectiveQuadraticCost (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)
	Construct a cost of the form (z_1^2 + z_2^2 + ... More...
	~PerspectiveQuadraticCost () override
const Eigen::MatrixXd &	A () const
const Eigen::VectorXd &	b () const
void	UpdateCoefficients (const Eigen::Ref< const Eigen::MatrixXd > &new_A, const Eigen::Ref< const Eigen::VectorXd > &new_b)
	Updates the coefficients of the cost. More...
Does not allow copy, move, or assignment
	PerspectiveQuadraticCost (const PerspectiveQuadraticCost &)=delete
PerspectiveQuadraticCost &	operator= (const PerspectiveQuadraticCost &)=delete
	PerspectiveQuadraticCost (PerspectiveQuadraticCost &&)=delete
PerspectiveQuadraticCost &	operator= (PerspectiveQuadraticCost &&)=delete
Public Member Functions inherited from Cost
	Cost (const Cost &)=delete
Cost &	operator= (const Cost &)=delete
	Cost (Cost &&)=delete
Cost &	operator= (Cost &&)=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
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::ostream &	DoDisplay (std::ostream &, const VectorX< symbolic::Variable > &) const override
	NVI implementation of Display. More...
std::string	DoToLatex (const VectorX< symbolic::Variable > &, int) const override
Protected Member Functions inherited from Cost
	Cost (int num_vars, const std::string &description="")
	Constructs a cost evaluator. More...
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)

Constructor & Destructor Documentation

PerspectiveQuadraticCost() [1/3]

PerspectiveQuadraticCost ( const PerspectiveQuadraticCost &  )

delete

PerspectiveQuadraticCost() [2/3]

PerspectiveQuadraticCost ( PerspectiveQuadraticCost &&  )

delete

PerspectiveQuadraticCost() [3/3]

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

Construct a cost of the form (z_1^2 + z_2^2 + ...

• z_{n-1}^2) / z_0 where z = Ax + b.

  Parameters

  A	Linear term.
  b	Constant term.

~PerspectiveQuadraticCost()

~PerspectiveQuadraticCost ( )

override

Member Function Documentation

A()

const Eigen::MatrixXd& A

(

)

const

b()

const Eigen::VectorXd& b

(

)

const

DoDisplay()

std::ostream& DoDisplay ( std::ostream &  os, const VectorX< symbolic::Variable > &  vars  ) const

overrideprotectedvirtual

NVI implementation of Display.

The default implementation will report the NiceTypeName, get_description, and list the bound variables. Subclasses may override to customize the message.

Precondition

vars size is consistent with num_vars".

Reimplemented from EvaluatorBase.

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.

DoToLatex()

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

overrideprotectedvirtual

Reimplemented from EvaluatorBase.

operator=() [1/2]

PerspectiveQuadraticCost& operator= ( PerspectiveQuadraticCost &&  )

delete

operator=() [2/2]

PerspectiveQuadraticCost& operator= ( const PerspectiveQuadraticCost &  )

delete

UpdateCoefficients()

void UpdateCoefficients	(	const Eigen::Ref< const Eigen::MatrixXd > &	new_A,
		const Eigen::Ref< const Eigen::VectorXd > &	new_b
	)

Updates the coefficients of the cost.

Note that the number of variables (columns of A) cannot change.

Parameters

new_A	New linear term.
new_b	New constant term.

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

• drake/solvers/cost.h