BoxQP Class Reference

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. More...
	~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. More...

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 82 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 17 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 69 of file box-qp.cpp.

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

• /root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/include/crocoddyl/core/solvers/box-qp.hpp
• /root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/src/core/solvers/box-qp.cpp