Namespaces
namespace	detail

namespace	linesearch

namespace	nb

namespace	preconditioner

Classes
struct	BackwardData
	This class stores the jacobians of PROXQP solvers with dense backends at a solutions wrt model parameters. More...

struct	BatchQP

struct	EigenAllowAlloc

struct	Model
	This class stores the model of the QP problem. More...

struct	QP

struct	QpView

struct	QpViewBox

struct	QpViewBoxMut

struct	QpViewMut

struct	Workspace
	This class defines the workspace of the dense solver. More...

Typedefs
template<typename T >
using	SparseMat = Eigen::SparseMatrix<T, 1>

template<typename T >
using	Vec = Eigen::Matrix<T, DYN, 1>

template<typename T >
using	VecRef = Eigen::Ref<Vec<T> const>

template<typename T >
using	VecRefMut = Eigen::Ref<Vec<T>>

template<typename T , int l = layout>
using	Mat = Eigen::Matrix<T, DYN, DYN, l>

template<typename T , int l = layout>
using	MatRef = Eigen::Ref<Mat<T, l> const>

template<typename T >
using	VecMap = Eigen::Map<Vec<T> const>

template<typename T >
using	VecMapMut = Eigen::Map<Vec<T>>

template<typename T , int l = layout>
using	MatMap = Eigen::Map<Mat<T, l> const>

template<typename T , int l = layout>
using	MatMapMut = Eigen::Map<Mat<T, l>>

using	VecMapISize = Eigen::Map<Eigen::Matrix<isize, DYN, 1> const>

using	VecISize = Eigen::Matrix<isize, DYN, 1>

using	VecMapBool = Eigen::Map<Eigen::Matrix<bool, DYN, 1> const>

using	VecBool = Eigen::Matrix<bool, DYN, 1>

Enumerations
enum	{ layout = Eigen::RowMajor }

Functions
template<typename T >
void	compute_backward (dense::QP< T > &solved_qp, VecRef< T > loss_derivative, T eps=1.E-4, T rho_new=1.E-6, T mu_new=1.E-6)

template<typename T >
void	compute_backward_loss_ESG (dense::QP< T > &solved_qp, VecRef< T > loss_derivative)

template<typename T , typename MatIn , typename VecIn1 , typename VecIn2 , typename VecIn3 >
T	power_iteration (const Eigen::MatrixBase< MatIn > &H, const Eigen::MatrixBase< VecIn1 > &dw, const Eigen::MatrixBase< VecIn2 > &rhs, const Eigen::MatrixBase< VecIn3 > &err_v, T power_iteration_accuracy, isize nb_power_iteration)

template<typename T , typename MatIn , typename VecIn1 , typename VecIn2 , typename VecIn3 >
T	min_eigen_value_via_modified_power_iteration (const Eigen::MatrixBase< MatIn > &H, const Eigen::MatrixBase< VecIn1 > &dw, const Eigen::MatrixBase< VecIn2 > &rhs, const Eigen::MatrixBase< VecIn3 > &err_v, T max_eigen_value, T power_iteration_accuracy, isize nb_power_iteration)

template<typename T , typename MatIn >
T	estimate_minimal_eigen_value_of_symmetric_matrix (const Eigen::MatrixBase< MatIn > &H, EigenValueEstimateMethodOption estimate_method_option, T power_iteration_accuracy, isize nb_power_iteration)

template<typename T >
void	update_default_rho_with_minimal_Hessian_eigen_value (optional< T > manual_minimal_H_eigenvalue, Results< T > &results, Settings< T > &settings)

template<typename T >
void	compute_equality_constrained_initial_guess (Workspace< T > &qpwork, const Settings< T > &qpsettings, const Model< T > &qpmodel, const isize n_constraints, const DenseBackend &dense_backend, const HessianType &hessian_type, Results< T > &qpresults)

template<typename T >
void	setup_factorization (Workspace< T > &qpwork, const Model< T > &qpmodel, Results< T > &qpresults, const DenseBackend &dense_backend, const HessianType &hessian_type)

template<typename T >
void	setup_equilibration (Workspace< T > &qpwork, const Settings< T > &qpsettings, const bool box_constraints, const HessianType hessian_type, preconditioner::RuizEquilibration< T > &ruiz, bool execute_preconditioner)

template<typename T >
void	initial_guess (Workspace< T > &qpwork, Settings< T > &qpsettings, Model< T > &qpmodel, Results< T > &qpresults)

template<typename T >
void	update (optional< MatRef< T > > H, optional< VecRef< T > > g, optional< MatRef< T > > A, optional< VecRef< T > > b, optional< MatRef< T > > C, optional< VecRef< T > > l, optional< VecRef< T > > u, optional< VecRef< T > > l_box, optional< VecRef< T > > u_box, Model< T > &model, Workspace< T > &work, const bool box_constraints)

template<typename T >
void	setup (optional< MatRef< T > > H, optional< VecRef< T > > g, optional< MatRef< T > > A, optional< VecRef< T > > b, optional< MatRef< T > > C, optional< VecRef< T > > l, optional< VecRef< T > > u, optional< VecRef< T > > l_box, optional< VecRef< T > > u_box, Settings< T > &qpsettings, Model< T > &qpmodel, Workspace< T > &qpwork, Results< T > &qpresults, const bool box_constraints, preconditioner::RuizEquilibration< T > &ruiz, PreconditionerStatus preconditioner_status, const HessianType hessian_type)

template<typename T >
void	update_proximal_parameters (Settings< T > &settings, Results< T > &results, Workspace< T > &work, optional< T > rho_new, optional< T > mu_eq_new, optional< T > mu_in_new)

template<typename T >
void	warm_start (optional< VecRef< T > > x_wm, optional< VecRef< T > > y_wm, optional< VecRef< T > > z_wm, Results< T > &results, Settings< T > &settings, Model< T > &model)

template<typename T >
bool	operator== (const Model< T > &model1, const Model< T > &model2)

template<typename T >
bool	operator!= (const Model< T > &model1, const Model< T > &model2)

template<typename T >
void	refactorize (const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const isize n_constraints, const DenseBackend &dense_backend, T rho_new)

template<typename T >
void	mu_update (const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, isize n_constraints, const DenseBackend &dense_backend, T mu_eq_new, T mu_in_new)

template<typename T >
void	iterative_residual (const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const isize n_constraints, isize inner_pb_dim, const HessianType &hessian_type)

template<typename T >
void	solve_linear_system (proxsuite::proxqp::dense::Vec< T > &dw, const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const isize n_constraints, const DenseBackend &dense_backend, isize inner_pb_dim, proxsuite::linalg::veg::dynstack::DynStackMut &stack)

template<typename T >
void	iterative_solve_with_permut_fact (const Settings< T > &qpsettings, const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const isize n_constraints, const DenseBackend &dense_backend, const HessianType &hessian_type, T eps, isize inner_pb_dim)

template<typename T >
void	bcl_update (const Settings< T > &qpsettings, Results< T > &qpresults, Workspace< T > &qpwork, T &primal_feasibility_lhs_new, T &bcl_eta_ext, T &bcl_eta_in, T bcl_eta_ext_init, T eps_in_min, T &new_bcl_mu_in, T &new_bcl_mu_eq, T &new_bcl_mu_in_inv, T &new_bcl_mu_eq_inv)

template<typename T >
void	Martinez_update (const Settings< T > &qpsettings, Results< T > &qpresults, T &primal_feasibility_lhs_new, T &primal_feasibility_lhs_old, T &bcl_eta_in, T eps_in_min, T &new_bcl_mu_in, T &new_bcl_mu_eq, T &new_bcl_mu_in_inv, T &new_bcl_mu_eq_inv)

template<typename T >
auto	compute_inner_loop_saddle_point (const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const Settings< T > &qpsettings) -> T

template<typename T >
void	primal_dual_semi_smooth_newton_step (const Settings< T > &qpsettings, const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const bool box_constraints, const isize n_constraints, const DenseBackend &dense_backend, const HessianType &hessian_type, T eps)

template<typename T >
void	primal_dual_newton_semi_smooth (const Settings< T > &qpsettings, const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const bool box_constraints, const isize n_constraints, preconditioner::RuizEquilibration< T > &ruiz, const DenseBackend &dense_backend, const HessianType &hessian_type, T eps_int)

template<typename T >
void	qp_solve (const Settings< T > &qpsettings, const Model< T > &qpmodel, Results< T > &qpresults, Workspace< T > &qpwork, const bool box_constraints, const DenseBackend &dense_backend, const HessianType &hessian_type, preconditioner::RuizEquilibration< T > &ruiz)

template<typename T >
void	print_setup_header (const Settings< T > &settings, const Results< T > &results, const Model< T > &model, const bool box_constraints, const DenseBackend &dense_backend, const HessianType &hessian_type)

template<typename Derived >
void	save_data (const std::string &filename, const ::Eigen::MatrixBase< Derived > &mat)

template<typename T >
void	global_primal_residual (const Model< T > &qpmodel, Results< T > &qpresults, const Settings< T > &qpsettings, Workspace< T > &qpwork, const preconditioner::RuizEquilibration< T > &ruiz, const bool box_constraints, T &primal_feasibility_lhs, T &primal_feasibility_eq_rhs_0, T &primal_feasibility_in_rhs_0, T &primal_feasibility_eq_lhs, T &primal_feasibility_in_lhs)

template<typename T >
bool	global_primal_residual_infeasibility (VectorViewMut< T > ATdy, VectorViewMut< T > CTdz, VectorViewMut< T > dy, VectorViewMut< T > dz, Workspace< T > &qpwork, const Model< T > &qpmodel, const Settings< T > &qpsettings, const bool box_constraints, const preconditioner::RuizEquilibration< T > &ruiz)

template<typename T >
bool	global_dual_residual_infeasibility (VectorViewMut< T > Adx, VectorViewMut< T > Cdx, VectorViewMut< T > Hdx, VectorViewMut< T > dx, Workspace< T > &qpwork, const Settings< T > &qpsettings, const Model< T > &qpmodel, const bool box_constraints, const preconditioner::RuizEquilibration< T > &ruiz)

template<typename T >
void	global_dual_residual (Results< T > &qpresults, Workspace< T > &qpwork, const Model< T > &qpmodel, const bool box_constraints, const preconditioner::RuizEquilibration< T > &ruiz, T &dual_feasibility_lhs, T &dual_feasibility_rhs_0, T &dual_feasibility_rhs_1, T &dual_feasibility_rhs_3, T &rhs_duality_gap, T &duality_gap, const HessianType &hessian_type)

	VEG_NIEBLOID (fabs)

	VEG_NIEBLOID (sqrt)

	VEG_NIEBLOID (pow)

	VEG_NIEBLOID (infty_norm)

template<typename T >
DenseBackend	dense_backend_choice (DenseBackend _dense_backend, isize dim, isize n_eq, isize n_in, bool box_constraints)
	This class defines the API of PROXQP solver with dense backend.

template<typename T >
proxqp::Results< T >	solve (optional< MatRef< T > > H, optional< VecRef< T > > g, optional< MatRef< T > > A, optional< VecRef< T > > b, optional< MatRef< T > > C, optional< VecRef< T > > l, optional< VecRef< T > > u, optional< VecRef< T > > x=nullopt, optional< VecRef< T > > y=nullopt, optional< VecRef< T > > z=nullopt, optional< T > eps_abs=nullopt, optional< T > eps_rel=nullopt, optional< T > rho=nullopt, optional< T > mu_eq=nullopt, optional< T > mu_in=nullopt, optional< bool > verbose=nullopt, bool compute_preconditioner=true, bool compute_timings=false, optional< isize > max_iter=nullopt, proxsuite::proxqp::InitialGuessStatus initial_guess=proxsuite::proxqp::InitialGuessStatus::EQUALITY_CONSTRAINED_INITIAL_GUESS, bool check_duality_gap=false, optional< T > eps_duality_gap_abs=nullopt, optional< T > eps_duality_gap_rel=nullopt, bool primal_infeasibility_solving=false, optional< T > manual_minimal_H_eigenvalue=nullopt)

template<typename T >
proxqp::Results< T >	solve (optional< MatRef< T > > H, optional< VecRef< T > > g, optional< MatRef< T > > A, optional< VecRef< T > > b, optional< MatRef< T > > C, optional< VecRef< T > > l, optional< VecRef< T > > u, optional< VecRef< T > > l_box, optional< VecRef< T > > u_box, optional< VecRef< T > > x=nullopt, optional< VecRef< T > > y=nullopt, optional< VecRef< T > > z=nullopt, optional< T > eps_abs=nullopt, optional< T > eps_rel=nullopt, optional< T > rho=nullopt, optional< T > mu_eq=nullopt, optional< T > mu_in=nullopt, optional< bool > verbose=nullopt, bool compute_preconditioner=true, bool compute_timings=false, optional< isize > max_iter=nullopt, proxsuite::proxqp::InitialGuessStatus initial_guess=proxsuite::proxqp::InitialGuessStatus::EQUALITY_CONSTRAINED_INITIAL_GUESS, bool check_duality_gap=false, optional< T > eps_duality_gap_abs=nullopt, optional< T > eps_duality_gap_rel=nullopt, bool primal_infeasibility_solving=false, optional< T > manual_minimal_H_eigenvalue=nullopt)

template<typename T >
bool	operator== (const QP< T > &qp1, const QP< T > &qp2)

template<typename T >
bool	operator!= (const QP< T > &qp1, const QP< T > &qp2)

template<typename T >
void	solve_in_parallel (std::vector< proxqp::dense::QP< T > > &qps, const optional< size_t > num_threads=nullopt)

template<typename T >
void	solve_in_parallel (proxqp::dense::BatchQP< T > &qps, const optional< size_t > num_threads=nullopt)

template<typename T >
void	qp_solve_in_parallel (optional< const size_t > num_threads, proxqp::dense::BatchQP< T > &qps)

template<typename T >
void	qp_solve_backward_in_parallel (optional< const size_t > num_threads, std::vector< proxqp::dense::QP< T > > &qps, std::vector< proxqp::dense::Vec< T > > &loss_derivatives, T eps=1.E-4, T rho_new=1.E-6, T mu_new=1.E-6)

template<typename T >
void	qp_solve_backward_in_parallel (optional< const size_t > num_threads, proxqp::dense::BatchQP< T > &qps, std::vector< proxqp::dense::Vec< T > > &loss_derivatives, T eps=1.E-4, T rho_new=1.E-6, T mu_new=1.E-6)

Variables
static constexpr auto	DYN = Eigen::Dynamic

Typedef Documentation

◆ SparseMat

template<typename T >

using proxsuite::proxqp::dense::SparseMat = Eigen::SparseMatrix<T, 1>

Definition at line 21 of file fwd.hpp.

◆ Vec

template<typename T >

using proxsuite::proxqp::dense::Vec = Eigen::Matrix<T, DYN, 1>

Definition at line 24 of file fwd.hpp.

◆ VecRef

template<typename T >

using proxsuite::proxqp::dense::VecRef = Eigen::Ref<Vec<T> const>

Definition at line 26 of file fwd.hpp.

◆ VecRefMut

template<typename T >

using proxsuite::proxqp::dense::VecRefMut = Eigen::Ref<Vec<T>>

Definition at line 28 of file fwd.hpp.

◆ Mat

template<typename T , int l = layout>

using proxsuite::proxqp::dense::Mat = Eigen::Matrix<T, DYN, DYN, l>

Definition at line 31 of file fwd.hpp.

◆ MatRef

template<typename T , int l = layout>

using proxsuite::proxqp::dense::MatRef = Eigen::Ref<Mat<T, l> const>

Definition at line 33 of file fwd.hpp.

◆ VecMap

template<typename T >

using proxsuite::proxqp::dense::VecMap = Eigen::Map<Vec<T> const>

Definition at line 38 of file fwd.hpp.

◆ VecMapMut

template<typename T >

using proxsuite::proxqp::dense::VecMapMut = Eigen::Map<Vec<T>>

Definition at line 40 of file fwd.hpp.

◆ MatMap

template<typename T , int l = layout>

using proxsuite::proxqp::dense::MatMap = Eigen::Map<Mat<T, l> const>

Definition at line 43 of file fwd.hpp.

◆ MatMapMut

template<typename T , int l = layout>

using proxsuite::proxqp::dense::MatMapMut = Eigen::Map<Mat<T, l>>

Definition at line 45 of file fwd.hpp.

◆ VecMapISize

using proxsuite::proxqp::dense::VecMapISize = Eigen::Map<Eigen::Matrix<isize, DYN, 1> const>

Definition at line 47 of file fwd.hpp.

◆ VecISize

using proxsuite::proxqp::dense::VecISize = Eigen::Matrix<isize, DYN, 1>

Definition at line 48 of file fwd.hpp.

◆ VecMapBool

using proxsuite::proxqp::dense::VecMapBool = Eigen::Map<Eigen::Matrix<bool, DYN, 1> const>

Definition at line 50 of file fwd.hpp.

◆ VecBool

using proxsuite::proxqp::dense::VecBool = Eigen::Matrix<bool, DYN, 1>

Definition at line 51 of file fwd.hpp.

Enumeration Type Documentation

◆ anonymous enum

anonymous enum

Enumerator
layout

Definition at line 16 of file fwd.hpp.

Function Documentation

◆ compute_backward()

template<typename T >

void proxsuite::proxqp::dense::compute_backward	(	dense::QP< T > &	solved_qp,
		VecRef< T >	loss_derivative,
		T	eps = 1.E-4,
		T	rho_new = 1.E-6,
		T	mu_new = 1.E-6 )

Computes the backward pass for the QP solver.

Parameters

solved_qp	The solved quadratic programming (QP) problem.
loss_derivative	The derivative of the loss function wrt the solution of the QP.
eps	The epsilon value for the iterative refinement, with a default value of 1.E-4.
rho_new	The new primal proximal parameter, with a default value of 1.E-6.
mu_new	The new dual proximal parameter used for both equality and inequality, with a default value of 1.E-6.

derive solution

Definition at line 31 of file compute_ECJ.hpp.

◆ compute_backward_loss_ESG()

template<typename T >

void proxsuite::proxqp::dense::compute_backward_loss_ESG	(	dense::QP< T > &	solved_qp,
		VecRef< T >	loss_derivative )

compute backward derivatives

Definition at line 129 of file compute_ECJ.hpp.

◆ power_iteration()

template<typename T , typename MatIn , typename VecIn1 , typename VecIn2 , typename VecIn3 >

T proxsuite::proxqp::dense::power_iteration	(	const Eigen::MatrixBase< MatIn > &	H,
		const Eigen::MatrixBase< VecIn1 > &	dw,
		const Eigen::MatrixBase< VecIn2 > &	rhs,
		const Eigen::MatrixBase< VecIn3 > &	err_v,
		T	power_iteration_accuracy,
		isize	nb_power_iteration )

Definition at line 30 of file helpers.hpp.

◆ min_eigen_value_via_modified_power_iteration()

template<typename T , typename MatIn , typename VecIn1 , typename VecIn2 , typename VecIn3 >

T proxsuite::proxqp::dense::min_eigen_value_via_modified_power_iteration	(	const Eigen::MatrixBase< MatIn > &	H,
		const Eigen::MatrixBase< VecIn1 > &	dw,
		const Eigen::MatrixBase< VecIn2 > &	rhs,
		const Eigen::MatrixBase< VecIn3 > &	err_v,
		T	max_eigen_value,
		T	power_iteration_accuracy,
		isize	nb_power_iteration )

Definition at line 71 of file helpers.hpp.

◆ estimate_minimal_eigen_value_of_symmetric_matrix()

template<typename T , typename MatIn >

T proxsuite::proxqp::dense::estimate_minimal_eigen_value_of_symmetric_matrix	(	const Eigen::MatrixBase< MatIn > &	H,
		EigenValueEstimateMethodOption	estimate_method_option,
		T	power_iteration_accuracy,
		isize	nb_power_iteration )

Estimate minimal eigenvalue of a symmetric Matrix

Parameters

H	symmetric matrix.
EigenValueEstimateMethodOption
power_iteration_accuracy	power iteration algorithm accuracy tracked
nb_power_iteration	maximal number of power iteration executed

Definition at line 125 of file helpers.hpp.

◆ update_default_rho_with_minimal_Hessian_eigen_value()

template<typename T >

void proxsuite::proxqp::dense::update_default_rho_with_minimal_Hessian_eigen_value	(	optional< T >	manual_minimal_H_eigenvalue,
		Results< T > &	results,
		Settings< T > &	settings )

Estimate H minimal eigenvalue

Parameters

settings	solver settings
results	solver results.
manual_minimal_H_eigenvalue	minimal H eigenvalue estimate.

Definition at line 176 of file helpers.hpp.

◆ compute_equality_constrained_initial_guess()

template<typename T >

void proxsuite::proxqp::dense::compute_equality_constrained_initial_guess	(	Workspace< T > &	qpwork,
		const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		const isize	n_constraints,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type,
		Results< T > &	qpresults )

Computes the equality constrained initial guess of a QP problem.

Parameters

qpwork	workspace of the solver.
qpsettings	settings of the solver.
qpmodel	QP problem as defined by the user (without any scaling performed).
qpresults	solution results.

Definition at line 201 of file helpers.hpp.

◆ setup_factorization()

template<typename T >

void proxsuite::proxqp::dense::setup_factorization	(	Workspace< T > &	qpwork,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type )

Setups and performs the first factorization of the regularized KKT matrix of the problem.

Parameters

qpwork	workspace of the solver.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solution results.

Definition at line 241 of file helpers.hpp.

◆ setup_equilibration()

template<typename T >

void proxsuite::proxqp::dense::setup_equilibration	(	Workspace< T > &	qpwork,
		const Settings< T > &	qpsettings,
		const bool	box_constraints,
		const HessianType	hessian_type,
		preconditioner::RuizEquilibration< T > &	ruiz,
		bool	execute_preconditioner )

Performs the equilibration of the QP problem for reducing its ill-conditionness.

Parameters

qpwork	workspace of the solver.
qpsettings	settings of the solver.
ruiz	ruiz preconditioner.
execute_preconditioner	boolean variable for executing or not the ruiz preconditioner. If set to False, it uses the previous preconditioning variables (initialized to the identity preconditioner if it is the first scaling performed).

Definition at line 300 of file helpers.hpp.

◆ initial_guess()

template<typename T >

void proxsuite::proxqp::dense::initial_guess	(	Workspace< T > &	qpwork,
		Settings< T > &	qpsettings,
		Model< T > &	qpmodel,
		Results< T > &	qpresults )

Setups the solver initial guess.

Parameters

qpwork	solver workspace.
qpsettings	solver settings.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.

Definition at line 342 of file helpers.hpp.

◆ update()

template<typename T >

void proxsuite::proxqp::dense::update	(	optional< MatRef< T > >	H,
		optional< VecRef< T > >	g,
		optional< MatRef< T > >	A,
		optional< VecRef< T > >	b,
		optional< MatRef< T > >	C,
		optional< VecRef< T > >	l,
		optional< VecRef< T > >	u,
		optional< VecRef< T > >	l_box,
		optional< VecRef< T > >	u_box,
		Model< T > &	model,
		Workspace< T > &	work,
		const bool	box_constraints )

Updates the QP solver model.

Parameters

H	quadratic cost input defining the QP model.
g	linear cost input defining the QP model.
A	equality constraint matrix input defining the QP model.
b	equality constraint vector input defining the QP model.
C	inequality constraint matrix input defining the QP model.
l	lower inequality constraint vector input defining the QP model.
u	upper inequality constraint vector input defining the QP model.
qpwork	solver workspace.
qpsettings	solver settings.
qpmodel	solver model.
qpresults	solver result.

Definition at line 374 of file helpers.hpp.

◆ setup()

template<typename T >

void proxsuite::proxqp::dense::setup	(	optional< MatRef< T > >	H,
		optional< VecRef< T > >	g,
		optional< MatRef< T > >	A,
		optional< VecRef< T > >	b,
		optional< MatRef< T > >	C,
		optional< VecRef< T > >	l,
		optional< VecRef< T > >	u,
		optional< VecRef< T > >	l_box,
		optional< VecRef< T > >	u_box,
		Settings< T > &	qpsettings,
		Model< T > &	qpmodel,
		Workspace< T > &	qpwork,
		Results< T > &	qpresults,
		const bool	box_constraints,
		preconditioner::RuizEquilibration< T > &	ruiz,
		PreconditionerStatus	preconditioner_status,
		const HessianType	hessian_type )

Setups the QP solver model.

Parameters

H	quadratic cost input defining the QP model.
g	linear cost input defining the QP model.
A	equality constraint matrix input defining the QP model.
b	equality constraint vector input defining the QP model.
C	inequality constraint matrix input defining the QP model.
l	lower inequality constraint vector input defining the QP model.
u	upper inequality constraint vector input defining the QP model.
qpwork	solver workspace.
qpsettings	solver settings.
qpmodel	solver model.
qpresults	solver result.
ruiz	ruiz preconditioner.
preconditioner_status	bool variable for deciding whether executing the preconditioning algorithm, or keeping previous preconditioning variables, or using the identity preconditioner (i.e., no preconditioner).

Definition at line 502 of file helpers.hpp.

◆ update_proximal_parameters()

template<typename T >

void proxsuite::proxqp::dense::update_proximal_parameters	(	Settings< T > &	settings,
		Results< T > &	results,
		Workspace< T > &	work,
		optional< T >	rho_new,
		optional< T >	mu_eq_new,
		optional< T >	mu_in_new )

Update the proximal parameters of the results object.

Parameters

rho_new	primal proximal parameter.
mu_eq_new	dual equality proximal parameter.
mu_in_new	dual inequality proximal parameter.
results	solver results.

Definition at line 680 of file helpers.hpp.

◆ warm_start()

template<typename T >

void proxsuite::proxqp::dense::warm_start	(	optional< VecRef< T > >	x_wm,
		optional< VecRef< T > >	y_wm,
		optional< VecRef< T > >	z_wm,
		Results< T > &	results,
		Settings< T > &	settings,
		Model< T > &	model )

Warm start the primal and dual variables.

Parameters

x_wm	primal warm start.
y_wm	dual equality warm start.
z_wm	dual inequality warm start.
results	solver result.
settings	solver settings.

Definition at line 717 of file helpers.hpp.

◆ operator==() [1/2]

template<typename T >

bool proxsuite::proxqp::dense::operator==	(	const Model< T > &	model1,
		const Model< T > &	model2 )

Definition at line 153 of file model.hpp.

◆ operator!=() [1/2]

template<typename T >

bool proxsuite::proxqp::dense::operator!=	(	const Model< T > &	model1,
		const Model< T > &	model2 )

Definition at line 167 of file model.hpp.

◆ refactorize()

template<typename T >

void proxsuite::proxqp::dense::refactorize	(	const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const isize	n_constraints,
		const DenseBackend &	dense_backend,
		T	rho_new )

Performs a refactorization of the KKT matrix used by the solver.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.
rho_new	new primal proximal parameter used for the refactorization.

Definition at line 40 of file solver.hpp.

◆ mu_update()

template<typename T >

void proxsuite::proxqp::dense::mu_update	(	const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		isize	n_constraints,
		const DenseBackend &	dense_backend,
		T	mu_eq_new,
		T	mu_in_new )

Updates the dual proximal parameters of the solver (i.e., penalization parameters of the primal-dual merit function).

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.
mu_eq_new	new dual equality constrained proximal parameter.
mu_in_new	new dual inequality constrained proximal parameter.

Definition at line 130 of file solver.hpp.

◆ iterative_residual()

template<typename T >

void proxsuite::proxqp::dense::iterative_residual	(	const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const isize	n_constraints,
		isize	inner_pb_dim,
		const HessianType &	hessian_type )

Derives the residual of the iterative refinement algorithm used for solving associated linear systems of PROXQP algorithm.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.
inner_pb_dim	dimension of the linear system.

Definition at line 245 of file solver.hpp.

◆ solve_linear_system()

template<typename T >

void proxsuite::proxqp::dense::solve_linear_system	(	proxsuite::proxqp::dense::Vec< T > &	dw,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const isize	n_constraints,
		const DenseBackend &	dense_backend,
		isize	inner_pb_dim,
		proxsuite::linalg::veg::dynstack::DynStackMut &	stack )

Definition at line 322 of file solver.hpp.

◆ iterative_solve_with_permut_fact()

template<typename T >

void proxsuite::proxqp::dense::iterative_solve_with_permut_fact	(	const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const isize	n_constraints,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type,
		T	eps,
		isize	inner_pb_dim )

Performs iterative refinement for solving associated linear systems of PROXQP algorithm.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpsettings	solver settings.
qpresults	solver results.
eps	accuracy required for pursuing or not the iterative refinement.
inner_pb_dim	dimension of the linear system.

Definition at line 408 of file solver.hpp.

◆ bcl_update()

template<typename T >

void proxsuite::proxqp::dense::bcl_update	(	const Settings< T > &	qpsettings,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		T &	primal_feasibility_lhs_new,
		T &	bcl_eta_ext,
		T &	bcl_eta_in,
		T	bcl_eta_ext_init,
		T	eps_in_min,
		T &	new_bcl_mu_in,
		T &	new_bcl_mu_eq,
		T &	new_bcl_mu_in_inv,
		T &	new_bcl_mu_eq_inv )

BCL rule for updating penalization parameters and accuracy variables.

Parameters

qpwork	solver workspace.
qpsettings	solver settings.
qpresults	solver results.
primal_feasibility_lhs_new	primal infeasibility.
bcl_eta_ext	BCL variable measuring whether the precisely infeasibility is too large or not.
bcl_eta_in	BCL variable setting the accuracy required for solving an associated subproblem.
bcl_eta_ext_init	initial BCL bcl_eta_ext variable value.
eps_in_min	minimal possible value for bcl_eta_in.
new_bcl_mu_in	new value of the inequality constrained penalization parameter.
new_bcl_mu_eq	new value of the equality constrained penalization parameter.
new_bcl_mu_in_inv	new value of the inequality constrained penalization parameter (inverse form).
new_bcl_mu_eq_inv	new value of the equality constrained penalization parameter (inverse form).

Definition at line 566 of file solver.hpp.

◆ Martinez_update()

template<typename T >

void proxsuite::proxqp::dense::Martinez_update	(	const Settings< T > &	qpsettings,
		Results< T > &	qpresults,
		T &	primal_feasibility_lhs_new,
		T &	primal_feasibility_lhs_old,
		T &	bcl_eta_in,
		T	eps_in_min,
		T &	new_bcl_mu_in,
		T &	new_bcl_mu_eq,
		T &	new_bcl_mu_in_inv,
		T &	new_bcl_mu_eq_inv )

Martinez rule for updating penalization parameters and accuracy variables.

Parameters

qpwork	solver workspace.
qpsettings	solver settings.
qpresults	solver results.
primal_feasibility_lhs_new	primal infeasibility.
bcl_eta_ext	BCL variable measuring whether the precisely infeasibility is too large or not.
bcl_eta_in	BCL variable setting the accuracy required for solving an associated subproblem.
bcl_eta_ext_init	initial BCL bcl_eta_ext variable value.
eps_in_min	minimal possible value for bcl_eta_in.
new_bcl_mu_in	new value of the inequality constrained penalization parameter.
new_bcl_mu_eq	new value of the equality constrained penalization parameter.
new_bcl_mu_in_inv	new value of the inequality constrained penalization parameter (inverse form).
new_bcl_mu_eq_inv	new value of the equality constrained penalization parameter (inverse form).

Definition at line 639 of file solver.hpp.

◆ compute_inner_loop_saddle_point()

template<typename T >

auto proxsuite::proxqp::dense::compute_inner_loop_saddle_point	(	const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const Settings< T > &	qpsettings ) -> T

Derives the stopping criterion value used by the Newton semismooth algorithm to minimize the primal-dual augmented Lagrangian function.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.

Definition at line 689 of file solver.hpp.

◆ primal_dual_semi_smooth_newton_step()

template<typename T >

void proxsuite::proxqp::dense::primal_dual_semi_smooth_newton_step	(	const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const bool	box_constraints,
		const isize	n_constraints,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type,
		T	eps )

Derives the Newton semismooth step.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpsettings	solver settings.
qpresults	solver results.
eps	accuracy required for solving the subproblem.

Definition at line 756 of file solver.hpp.

◆ primal_dual_newton_semi_smooth()

template<typename T >

void proxsuite::proxqp::dense::primal_dual_newton_semi_smooth	(	const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const bool	box_constraints,
		const isize	n_constraints,
		preconditioner::RuizEquilibration< T > &	ruiz,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type,
		T	eps_int )

Performs the Newton semismooth algorithm to minimize the primal-dual augmented Lagrangian function used by PROXQP algorithm.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpsettings	solver settings.
qpresults	solver results.
ruiz	ruiz preconditioner.
eps_int	accuracy required for solving the subproblem.

Definition at line 884 of file solver.hpp.

◆ qp_solve()

template<typename T >

void proxsuite::proxqp::dense::qp_solve	(	const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const bool	box_constraints,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type,
		preconditioner::RuizEquilibration< T > &	ruiz )

Executes the PROXQP algorithm.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpsettings	solver settings.
qpresults	solver results.
ruiz	ruiz preconditioner.

\ TODO in a quicker way

effective mu upddate

Definition at line 1090 of file solver.hpp.

◆ print_setup_header()

template<typename T >

void proxsuite::proxqp::dense::print_setup_header	(	const Settings< T > &	settings,
		const Results< T > &	results,
		const Model< T > &	model,
		const bool	box_constraints,
		const DenseBackend &	dense_backend,
		const HessianType &	hessian_type )

Definition at line 33 of file utils.hpp.

◆ save_data()

template<typename Derived >

void proxsuite::proxqp::dense::save_data	(	const std::string &	filename,
		const ::Eigen::MatrixBase< Derived > &	mat )

Save a matrix into a CSV format. Used for debug purposes.

Parameters

filename	filename name for the CSV.
mat	matrix to save into CSV format.

Definition at line 133 of file utils.hpp.

◆ global_primal_residual()

template<typename T >

void proxsuite::proxqp::dense::global_primal_residual	(	const Model< T > &	qpmodel,
		Results< T > &	qpresults,
		const Settings< T > &	qpsettings,
		Workspace< T > &	qpwork,
		const preconditioner::RuizEquilibration< T > &	ruiz,
		const bool	box_constraints,
		T &	primal_feasibility_lhs,
		T &	primal_feasibility_eq_rhs_0,
		T &	primal_feasibility_in_rhs_0,
		T &	primal_feasibility_eq_lhs,
		T &	primal_feasibility_in_lhs )

Derives the global primal residual of the QP problem.

Parameters

qpwork	solver workspace.
qpmodel	QP problem model as defined by the user (without any scaling performed).
qpresults	solver results.
ruiz	ruiz preconditioner.
primal_feasibility_lhs	primal infeasibility.
primal_feasibility_eq_rhs_0	scalar variable used when using a relative stopping criterion.
primal_feasibility_in_rhs_0	scalar variable used when using a relative stopping criterion.
primal_feasibility_eq_lhs	scalar variable used when using a relative stopping criterion.
primal_feasibility_in_lhs	scalar variable used when using a relative stopping criterion.

Definition at line 166 of file utils.hpp.

◆ global_primal_residual_infeasibility()

template<typename T >

bool proxsuite::proxqp::dense::global_primal_residual_infeasibility	(	VectorViewMut< T >	ATdy,
		VectorViewMut< T >	CTdz,
		VectorViewMut< T >	dy,
		VectorViewMut< T >	dz,
		Workspace< T > &	qpwork,
		const Model< T > &	qpmodel,
		const Settings< T > &	qpsettings,
		const bool	box_constraints,
		const preconditioner::RuizEquilibration< T > &	ruiz )

Check whether the global primal infeasibility criterion is satisfied.

Parameters

qpwork	solver workspace.
qpsettings	solver settings.
ruiz	ruiz preconditioner.
ATdy	variable used for testing global primal infeasibility criterion is satisfied.
CTdz	variable used for testing global primal infeasibility criterion is satisfied.
dy	variable used for testing global primal infeasibility criterion is satisfied.
dz	variable used for testing global primal infeasibility criterion is satisfied.

Definition at line 271 of file utils.hpp.

◆ global_dual_residual_infeasibility()

template<typename T >

bool proxsuite::proxqp::dense::global_dual_residual_infeasibility	(	VectorViewMut< T >	Adx,
		VectorViewMut< T >	Cdx,
		VectorViewMut< T >	Hdx,
		VectorViewMut< T >	dx,
		Workspace< T > &	qpwork,
		const Settings< T > &	qpsettings,
		const Model< T > &	qpmodel,
		const bool	box_constraints,
		const preconditioner::RuizEquilibration< T > &	ruiz )

Check whether the global dual infeasibility criterion is satisfied.

Parameters

qpwork	solver workspace.
qpsettings	solver settings.
qpmodel	QP problem model as defined by the user (without any scaling performed).
ruiz	ruiz preconditioner.
Adx	variable used for testing global dual infeasibility criterion is satisfied.
Cdx	variable used for testing global dual infeasibility criterion is satisfied.
Hdx	variable used for testing global dual infeasibility criterion is satisfied.
dx	variable used for testing global dual infeasibility criterion is satisfied.

Definition at line 345 of file utils.hpp.

◆ global_dual_residual()

template<typename T >

void proxsuite::proxqp::dense::global_dual_residual	(	Results< T > &	qpresults,
		Workspace< T > &	qpwork,
		const Model< T > &	qpmodel,
		const bool	box_constraints,
		const preconditioner::RuizEquilibration< T > &	ruiz,
		T &	dual_feasibility_lhs,
		T &	dual_feasibility_rhs_0,
		T &	dual_feasibility_rhs_1,
		T &	dual_feasibility_rhs_3,
		T &	rhs_duality_gap,
		T &	duality_gap,
		const HessianType &	hessian_type )

Derives the global dual residual of the QP problem.

Parameters

qpwork	solver workspace.
qpresults	solver results.
ruiz	ruiz preconditioner.
dual_feasibility_lhs	primal infeasibility.
primal_feasibility_eq_rhs_0	scalar variable used when using a relative stopping criterion.
dual_feasibility_rhs_0	scalar variable used when using a relative stopping criterion.
dual_feasibility_rhs_1	scalar variable used when using a relative stopping criterion.
dual_feasibility_rhs_3	scalar variable used when using a relative stopping criterion.

Definition at line 439 of file utils.hpp.

◆ VEG_NIEBLOID() [1/4]

proxsuite::proxqp::dense::VEG_NIEBLOID ( fabs )

◆ VEG_NIEBLOID() [2/4]

proxsuite::proxqp::dense::VEG_NIEBLOID ( sqrt )

◆ VEG_NIEBLOID() [3/4]

proxsuite::proxqp::dense::VEG_NIEBLOID ( pow )

◆ VEG_NIEBLOID() [4/4]

proxsuite::proxqp::dense::VEG_NIEBLOID ( infty_norm )

◆ dense_backend_choice()

template<typename T >

DenseBackend proxsuite::proxqp::dense::dense_backend_choice	(	DenseBackend	_dense_backend,
		isize	dim,
		isize	n_eq,
		isize	n_in,
		bool	box_constraints )

This class defines the API of PROXQP solver with dense backend.

Wrapper class for using proxsuite API with dense backend for solving linearly constrained convex QP problem using ProxQp algorithm.

Example usage:

#include <Eigen/Core>
#include <Eigen/Cholesky>
#include <proxsuite/proxqp/dense/dense.hpp>
#include <proxsuite/linalg/veg/util/dbg.hpp>
#include <util.hpp>
 
using T = double;
auto main() -> int {
 
        // Generate a random QP problem with primal variable dimension of size
dim; n_eq equality constraints and n_in inequality constraints
        ::proxsuite::proxqp::test::rand::set_seed(1);
        proxqp::isize dim = 10;
        proxqp::isize n_eq(dim / 4);
        proxqp::isize n_in(dim / 4);
        T strong_convexity_factor(1.e-2);
        T sparsity_factor = 0.15; // controls the sparsity of each matrix of the
problem generated T eps_abs = T(1e-9); Qp<T> qp{
                        random_with_dim_and_neq_and_n_in,
                        dim,
                        n_eq,
                        n_in,
                        sparsity_factor,
                        strong_convexity_factor};
 
        // Solve the problem
        proxqp::dense::QP<T> Qp{dim, n_eq, n_in}; // creating QP object
        Qp.settings.eps_abs = eps_abs; // choose accuracy needed
        Qp.init(qp.H, qp.g, qp.A, qp.b, qp.C, qp.u, qp.l); // setup the QP
object Qp.solve(); // solve the problem
 
        // Verify solution accuracy
        T pri_res = std::max(
                        (qp.A * Qp.results.x - qp.b).lpNorm<Eigen::Infinity>(),
                        (helpers::positive_part(qp.C * Qp.results.x -
qp.u) + helpers::negative_part(qp.C * Qp.results.x - qp.l))
                                        .lpNorm<Eigen::Infinity>());
        T dua_res = (qp.H * Qp.results.x + qp.g + qp.A.transpose() *
Qp.results.y + qp.C.transpose() * Qp.results.z) .lpNorm<Eigen::Infinity>();
        VEG_ASSERT(pri_res <= eps_abs);
        VEG_ASSERT(dua_res <= eps_abs);
 
        // Some solver statistics
        std::cout << "------solving qp with dim: " << dim
                                                << " neq: " << n_eq << " nin: "
<< n_in << std::endl; std::cout << "primal residual: " << pri_res << std::endl;
        std::cout << "dual residual: " << dua_res << std::endl;
        std::cout << "total number of iteration: " << Qp.results.info.iter
                                                << std::endl;
}

Definition at line 83 of file wrapper.hpp.

◆ solve() [1/2]

template<typename T >

proxqp::Results< T > proxsuite::proxqp::dense::solve	(	optional< MatRef< T > >	H,
		optional< VecRef< T > >	g,
		optional< MatRef< T > >	A,
		optional< VecRef< T > >	b,
		optional< MatRef< T > >	C,
		optional< VecRef< T > >	l,
		optional< VecRef< T > >	u,
		optional< VecRef< T > >	x = nullopt,
		optional< VecRef< T > >	y = nullopt,
		optional< VecRef< T > >	z = nullopt,
		optional< T >	eps_abs = nullopt,
		optional< T >	eps_rel = nullopt,
		optional< T >	rho = nullopt,
		optional< T >	mu_eq = nullopt,
		optional< T >	mu_in = nullopt,
		optional< bool >	verbose = nullopt,
		bool	compute_preconditioner = true,
		bool	compute_timings = false,
		optional< isize >	max_iter = nullopt,
		proxsuite::proxqp::InitialGuessStatus	initial_guess = proxsuite::proxqp::InitialGuessStatus::EQUALITY_CONSTRAINED_INITIAL_GUESS,
		bool	check_duality_gap = false,
		optional< T >	eps_duality_gap_abs = nullopt,
		optional< T >	eps_duality_gap_rel = nullopt,
		bool	primal_infeasibility_solving = false,
		optional< T >	manual_minimal_H_eigenvalue = nullopt )

Solves the QP problem using PROXQP algorithm without the need to define a QP object, with matrices defined by Dense Eigen matrices. It is possible to set up some of the solver parameters (warm start, initial guess option, proximal step sizes, absolute and relative accuracies, maximum number of iterations, preconditioner execution). There are no box constraints in the model.

Parameters

H	quadratic cost input defining the QP model.
g	linear cost input defining the QP model.
A	equality constraint matrix input defining the QP model.
b	equality constraint vector input defining the QP model.
C	inequality constraint matrix input defining the QP model.
l	lower inequality constraint vector input defining the QP model.
u	upper inequality constraint vector input defining the QP model.
x	primal warm start.
y	dual equality constraint warm start.
z	dual inequality constraint warm start.
verbose	if set to true, the solver prints more information about each iteration.
compute_preconditioner	bool parameter for executing or not the preconditioner.
compute_timings	boolean parameter for computing the solver timings.
rho	proximal step size wrt primal variable.
mu_eq	proximal step size wrt equality constrained multiplier.
mu_in	proximal step size wrt inequality constrained multiplier.
eps_abs	absolute accuracy threshold.
eps_rel	relative accuracy threshold.
max_iter	maximum number of iteration.
initial_guess	initial guess option for warm starting or not the initial iterate values.
check_duality_gap	If set to true, include the duality gap in absolute and relative stopping criteria.
eps_duality_gap_abs	absolute accuracy threshold for the duality-gap criterion.
eps_duality_gap_rel	relative accuracy threshold for the duality-gap criterion.

Definition at line 1002 of file wrapper.hpp.

◆ solve() [2/2]

template<typename T >

proxqp::Results< T > proxsuite::proxqp::dense::solve	(	optional< MatRef< T > >	H,
		optional< VecRef< T > >	g,
		optional< MatRef< T > >	A,
		optional< VecRef< T > >	b,
		optional< MatRef< T > >	C,
		optional< VecRef< T > >	l,
		optional< VecRef< T > >	u,
		optional< VecRef< T > >	l_box,
		optional< VecRef< T > >	u_box,
		optional< VecRef< T > >	x = nullopt,
		optional< VecRef< T > >	y = nullopt,
		optional< VecRef< T > >	z = nullopt,
		optional< T >	eps_abs = nullopt,
		optional< T >	eps_rel = nullopt,
		optional< T >	rho = nullopt,
		optional< T >	mu_eq = nullopt,
		optional< T >	mu_in = nullopt,
		optional< bool >	verbose = nullopt,
		bool	compute_preconditioner = true,
		bool	compute_timings = false,
		optional< isize >	max_iter = nullopt,
		proxsuite::proxqp::InitialGuessStatus	initial_guess = proxsuite::proxqp::InitialGuessStatus::EQUALITY_CONSTRAINED_INITIAL_GUESS,
		bool	check_duality_gap = false,
		optional< T >	eps_duality_gap_abs = nullopt,
		optional< T >	eps_duality_gap_rel = nullopt,
		bool	primal_infeasibility_solving = false,
		optional< T >	manual_minimal_H_eigenvalue = nullopt )

Solves the QP problem using PROXQP algorithm without the need to define a QP object, with matrices defined by Dense Eigen matrices. It is possible to set up some of the solver parameters (warm start, initial guess option, proximal step sizes, absolute and relative accuracies, maximum number of iterations, preconditioner execution).

Parameters

H	quadratic cost input defining the QP model.
g	linear cost input defining the QP model.
A	equality constraint matrix input defining the QP model.
b	equality constraint vector input defining the QP model.
C	inequality constraint matrix input defining the QP model.
l	lower inequality constraint vector input defining the QP model.
u	upper inequality constraint vector input defining the QP model.
l_box	lower box inequality constraint vector input defining the QP model.
u_box	upper box inequality constraint vector input defining the QP model.
x	primal warm start.
y	dual equality constraint warm start.
z	dual inequality constraint warm start. The upper part must contain a warm start for inequality constraints wrt C matrix, whereas the latter wrt the box inequalities.
verbose	if set to true, the solver prints more information about each iteration.
compute_preconditioner	bool parameter for executing or not the preconditioner.
compute_timings	boolean parameter for computing the solver timings.
rho	proximal step size wrt primal variable.
mu_eq	proximal step size wrt equality constrained multiplier.
mu_in	proximal step size wrt inequality constrained multiplier.
eps_abs	absolute accuracy threshold.
eps_rel	relative accuracy threshold.
max_iter	maximum number of iteration.
initial_guess	initial guess option for warm starting or not the initial iterate values.
check_duality_gap	If set to true, include the duality gap in absolute and relative stopping criteria.
eps_duality_gap_abs	absolute accuracy threshold for the duality-gap criterion.
eps_duality_gap_rel	relative accuracy threshold for the duality-gap criterion.

Definition at line 1132 of file wrapper.hpp.

◆ operator==() [2/2]

template<typename T >

bool proxsuite::proxqp::dense::operator==	(	const QP< T > &	qp1,
		const QP< T > &	qp2 )

Definition at line 1237 of file wrapper.hpp.

◆ operator!=() [2/2]

template<typename T >

bool proxsuite::proxqp::dense::operator!=	(	const QP< T > &	qp1,
		const QP< T > &	qp2 )

Definition at line 1247 of file wrapper.hpp.

◆ solve_in_parallel() [1/2]

template<typename T >

void proxsuite::proxqp::dense::solve_in_parallel	(	std::vector< proxqp::dense::QP< T > > &	qps,
		const optional< size_t >	num_threads = nullopt )

Definition at line 19 of file qp_solve.hpp.

◆ solve_in_parallel() [2/2]

template<typename T >

void proxsuite::proxqp::dense::solve_in_parallel	(	proxqp::dense::BatchQP< T > &	qps,
		const optional< size_t >	num_threads = nullopt )

Definition at line 42 of file qp_solve.hpp.

◆ qp_solve_in_parallel()

template<typename T >

void proxsuite::proxqp::dense::qp_solve_in_parallel	(	optional< const size_t >	num_threads,
		proxqp::dense::BatchQP< T > &	qps )

Definition at line 64 of file qp_solve.hpp.

◆ qp_solve_backward_in_parallel() [1/2]

template<typename T >

void proxsuite::proxqp::dense::qp_solve_backward_in_parallel	(	optional< const size_t >	num_threads,
		std::vector< proxqp::dense::QP< T > > &	qps,
		std::vector< proxqp::dense::Vec< T > > &	loss_derivatives,
		T	eps = 1.E-4,
		T	rho_new = 1.E-6,
		T	mu_new = 1.E-6 )

Definition at line 86 of file qp_solve.hpp.

◆ qp_solve_backward_in_parallel() [2/2]

template<typename T >

void proxsuite::proxqp::dense::qp_solve_backward_in_parallel	(	optional< const size_t >	num_threads,
		proxqp::dense::BatchQP< T > &	qps,
		std::vector< proxqp::dense::Vec< T > > &	loss_derivatives,
		T	eps = 1.E-4,
		T	rho_new = 1.E-6,
		T	mu_new = 1.E-6 )

Definition at line 114 of file qp_solve.hpp.

Variable Documentation

◆ DYN

constexpr auto proxsuite::proxqp::dense::DYN = Eigen::Dynamic

staticconstexpr

Definition at line 15 of file fwd.hpp.

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ SparseMat

◆ Vec

◆ VecRef

◆ VecRefMut

◆ Mat

◆ MatRef

◆ VecMap

◆ VecMapMut

◆ MatMap

◆ MatMapMut

◆ VecMapISize

◆ VecISize

◆ VecMapBool

◆ VecBool

Enumeration Type Documentation

◆ anonymous enum

Function Documentation

◆ compute_backward()

◆ compute_backward_loss_ESG()

◆ power_iteration()

◆ min_eigen_value_via_modified_power_iteration()

◆ estimate_minimal_eigen_value_of_symmetric_matrix()

◆ update_default_rho_with_minimal_Hessian_eigen_value()

◆ compute_equality_constrained_initial_guess()

◆ setup_factorization()

◆ setup_equilibration()

◆ initial_guess()

◆ update()

◆ setup()

◆ update_proximal_parameters()

◆ warm_start()

◆ operator==() [1/2]

◆ operator!=() [1/2]

◆ refactorize()

◆ mu_update()

◆ iterative_residual()

◆ solve_linear_system()

◆ iterative_solve_with_permut_fact()

◆ bcl_update()

◆ Martinez_update()

◆ compute_inner_loop_saddle_point()

◆ primal_dual_semi_smooth_newton_step()

◆ primal_dual_newton_semi_smooth()

◆ qp_solve()

◆ print_setup_header()

◆ save_data()

◆ global_primal_residual()

◆ global_primal_residual_infeasibility()

◆ global_dual_residual_infeasibility()

◆ global_dual_residual()

◆ VEG_NIEBLOID() [1/4]

◆ VEG_NIEBLOID() [2/4]

◆ VEG_NIEBLOID() [3/4]

◆ VEG_NIEBLOID() [4/4]

◆ dense_backend_choice()

◆ solve() [1/2]

◆ solve() [2/2]

◆ operator==() [2/2]

◆ operator!=() [2/2]

◆ solve_in_parallel() [1/2]

◆ solve_in_parallel() [2/2]

◆ qp_solve_in_parallel()

◆ qp_solve_backward_in_parallel() [1/2]

◆ qp_solve_backward_in_parallel() [2/2]

Variable Documentation

◆ DYN