This class implements a Box QP solver based on a Projected Newton method. More...

#include <box-qp.hpp>

Public Types
typedef BoxQPSolutionTpl< Scalar >	BoxQPSolution
typedef MathBaseTpl< Scalar >	MathBase
typedef MathBase::MatrixXs	MatrixXs
typedef MathBase::VectorXs	VectorXs

Public Member Functions
	BoxQPTpl (const std::size_t nx, const std::size_t maxiter=100, const Scalar th_acceptstep=Scalar(0.1), const Scalar th_grad=Scalar(1e-9), const Scalar reg=Scalar(1e-9))
	Initialize the Projected-Newton QP for bound constraints.
	~BoxQPTpl ()=default
	Destroy the Projected-Newton QP solver.
template<typename NewScalar>
BoxQPTpl< NewScalar >	cast () const
	Cast the BoxQP solver to a different scalar type.
const std::vector< Scalar > &	get_alphas () const
	Return the stack of step lengths using by the line-search procedure.
std::size_t	get_maxiter () const
	Return the maximum allowed number of iterations.
std::size_t	get_nx () const
	Return the decision vector dimension.
Scalar	get_reg () const
	Return the regularization value.
const BoxQPSolution &	get_solution () const
	Return the stored solution.
Scalar	get_th_acceptstep () const
	Return the acceptance step threshold.
Scalar	get_th_grad () const
	Return the gradient tolerance threshold.
void	set_alphas (const std::vector< Scalar > &alphas)
	Modify the stack of step lengths using by the line-search procedure.
void	set_maxiter (const std::size_t maxiter)
	Modify the maximum allowed number of iterations.
void	set_nx (const std::size_t nx)
	Modify the decision vector dimension.
void	set_reg (const Scalar reg)
	Modify the regularization value.
void	set_th_acceptstep (const Scalar th_acceptstep)
	Modify the acceptance step threshold.
void	set_th_grad (const Scalar th_grad)
	Modify the gradient tolerance threshold.
const BoxQPSolution &	solve (const MatrixXs &H, const VectorXs &q, const VectorXs &lb, const VectorXs &ub, const VectorXs &xinit)
	Compute the solution of bound-constrained QP based on Newton projection.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Detailed Description

template<typename _Scalar>
class crocoddyl::BoxQPTpl< _Scalar >

This class implements a Box QP solver based on a Projected Newton method.

We consider a box QP problem of the form:

$\begin{eqnarray*} \min_{\mathbf{x}} &= \frac{1}{2}\mathbf{x}^T\mathbf{H}\mathbf{x} + \mathbf{q}^T\mathbf{x} \\ \textrm{subject to} & \hspace{1em} \mathbf{\underline{b}} \leq \mathbf{x} \leq \mathbf{\bar{b}} \\ \end{eqnarray*}$

where $\mathbf{H}$ , $\mathbf{q}$ are the Hessian and gradient of the problem, respectively, $\mathbf{\underline{b}}$ , $\mathbf{\bar{b}}$ are lower and upper bounds of the decision variable $\mathbf{x}$ .

The algorithm procees by iteratively identifying the active bounds, and then performing a projected Newton step in the free sub-space. The projection uses the Hessian of the free sub-space and is computed efficiently using a Cholesky decomposition. It uses a line search procedure with polynomial step length values in a backtracking fashion. The steps are checked using an Armijo condition together L2-norm gradient.

For more details about this solver, we encourage you to read the following article:

Definition at line 103 of file box-qp.hpp.

Member Typedef Documentation

◆ BoxQPSolution

template<typename _Scalar>

typedef BoxQPSolutionTpl<Scalar> BoxQPSolution

Definition at line 108 of file box-qp.hpp.

◆ MathBase

template<typename _Scalar>

typedef MathBaseTpl<Scalar> MathBase

Definition at line 109 of file box-qp.hpp.

◆ VectorXs

template<typename _Scalar>

typedef MathBase::VectorXs VectorXs

Definition at line 110 of file box-qp.hpp.

◆ MatrixXs

template<typename _Scalar>

typedef MathBase::MatrixXs MatrixXs

Definition at line 111 of file box-qp.hpp.

Constructor & Destructor Documentation

◆ BoxQPTpl()

template<typename _Scalar>

BoxQPTpl	(	const std::size_t	nx,
		const std::size_t	maxiter = 100,
		const Scalar	th_acceptstep = Scalar(0.1),
		const Scalar	th_grad = Scalar(1e-9),
		const Scalar	reg = Scalar(1e-9) )

Initialize the Projected-Newton QP for bound constraints.

Parameters

[in]	nx	Dimension of the decision vector
[in]	maxiter	Maximum number of allowed iterations (default 100)
[in]	th_acceptstep	Acceptance step threshold (default 0.1)
[in]	th_grad	Gradient tolerance threshold (default 1e-9)
[in]	reg	Regularization value (default 1e-9)

Member Function Documentation

◆ solve()

template<typename _Scalar>

const BoxQPSolution & solve	(	const MatrixXs &	H,
		const VectorXs &	q,
		const VectorXs &	lb,
		const VectorXs &	ub,
		const VectorXs &	xinit )

Compute the solution of bound-constrained QP based on Newton projection.

Parameters

[in]	H	Hessian (dimension nx * nx)
[in]	q	Gradient (dimension nx)
[in]	lb	Lower bound (dimension nx)
[in]	ub	Upper bound (dimension nx)
[in]	xinit	Initial guess (dimension nx)

Returns: The solution of the problem

◆ cast()

template<typename _Scalar>

template<typename NewScalar>

BoxQPTpl< NewScalar > cast ( ) const

Cast the BoxQP solver to a different scalar type.

It is useful for operations requiring different precision or scalar types.

Template Parameters

NewScalar The new scalar type to cast to.

Returns: BoxQPTpl<NewScalar> A BoxQP solver with the new scalar type.

Member Data Documentation

◆ Scalar

template<typename _Scalar>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Definition at line 107 of file box-qp.hpp.

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

/build/source/include/crocoddyl/core/fwd.hpp
/build/source/include/crocoddyl/core/solvers/box-qp.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ BoxQPSolution

◆ MathBase

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ BoxQPTpl()

Member Function Documentation

◆ solve()

◆ cast()

Member Data Documentation

◆ Scalar