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

#include <box-qp.hpp>

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	BoxQP (const std::size_t nx, const std::size_t maxiter=100, const double th_acceptstep=0.1, const double th_grad=1e-9, const double reg=1e-9)
	Initialize the Projected-Newton QP for bound constraints.
	~BoxQP ()
	Destroy the Projected-Newton QP solver.
const std::vector< double > &	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.
double	get_reg () const
	Return the regularization value.
const BoxQPSolution &	get_solution () const
	Return the stored solution.
double	get_th_acceptstep () const
	Return the acceptance step threshold.
double	get_th_grad () const
	Return the gradient tolerance threshold.
void	set_alphas (const std::vector< double > &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 double reg)
	Modify the regularization value.
void	set_th_acceptstep (const double th_acceptstep)
	Modify the acceptance step threshold.
void	set_th_grad (const double th_grad)
	Modify the gradient tolerance threshold.
const BoxQPSolution &	solve (const Eigen::MatrixXd &H, const Eigen::VectorXd &q, const Eigen::VectorXd &lb, const Eigen::VectorXd &ub, const Eigen::VectorXd &xinit)
	Compute the solution of bound-constrained QP based on Newton projection.

Detailed Description

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 79 of file box-qp.hpp.

Constructor & Destructor Documentation

◆ BoxQP()

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

Definition at line 13 of file box-qp.cpp.

◆ ~BoxQP()

~BoxQP ( )

Destroy the Projected-Newton QP solver.

Definition at line 63 of file box-qp.cpp.

Member Function Documentation

◆ solve()

const BoxQPSolution & solve	(	const Eigen::MatrixXd &	H,
		const Eigen::VectorXd &	q,
		const Eigen::VectorXd &	lb,
		const Eigen::VectorXd &	ub,
		const Eigen::VectorXd &	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

Definition at line 65 of file box-qp.cpp.

◆ get_solution()

const BoxQPSolution & get_solution ( ) const

Return the stored solution.

Definition at line 191 of file box-qp.cpp.

◆ get_nx()

std::size_t get_nx ( ) const

Return the decision vector dimension.

Definition at line 193 of file box-qp.cpp.

◆ get_maxiter()

std::size_t get_maxiter ( ) const

Return the maximum allowed number of iterations.

Definition at line 195 of file box-qp.cpp.

◆ get_th_acceptstep()

double get_th_acceptstep ( ) const

Return the acceptance step threshold.

Definition at line 197 of file box-qp.cpp.

◆ get_th_grad()

double get_th_grad ( ) const

Return the gradient tolerance threshold.

Definition at line 199 of file box-qp.cpp.

◆ get_reg()

double get_reg ( ) const

Return the regularization value.

Definition at line 201 of file box-qp.cpp.

◆ get_alphas()

const std::vector< double > & get_alphas ( ) const

Return the stack of step lengths using by the line-search procedure.

Definition at line 203 of file box-qp.cpp.

◆ set_nx()

void set_nx ( const std::size_t nx )

Modify the decision vector dimension.

Definition at line 205 of file box-qp.cpp.

◆ set_maxiter()

void set_maxiter ( const std::size_t maxiter )

Modify the maximum allowed number of iterations.

Definition at line 217 of file box-qp.cpp.

◆ set_th_acceptstep()

void set_th_acceptstep ( const double th_acceptstep )

Modify the acceptance step threshold.

Definition at line 219 of file box-qp.cpp.

◆ set_th_grad()

void set_th_grad ( const double th_grad )

Modify the gradient tolerance threshold.

Definition at line 227 of file box-qp.cpp.

◆ set_reg()

void set_reg ( const double reg )

Modify the regularization value.

Definition at line 234 of file box-qp.cpp.

◆ set_alphas()

void set_alphas ( const std::vector< double > & alphas )

Modify the stack of step lengths using by the line-search procedure.

Definition at line 241 of file box-qp.cpp.

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

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

Public Member Functions