Class for interfacing a crocoddyl::ShootingProblem with IPOPT. More...

#include <ipopt-iface.hpp>

Inheritance diagram for IpoptInterface:

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	IpoptInterface (const boost::shared_ptr< crocoddyl::ShootingProblem > &problem)
	Initialize the Ipopt interface. More...

boost::shared_ptr< IpoptInterfaceData >	createData (const std::size_t nx, const std::size_t ndx, const std::size_t nu)
	Create the data structure to store temporary computations. More...

virtual bool	eval_f (Ipopt::Index n, const Ipopt::Number *x, bool new_x, Ipopt::Number &obj_value)
	Method to request the value of the objective function. More...

virtual bool	eval_g (Ipopt::Index n, const Ipopt::Number x, bool new_x, Ipopt::Index m, Ipopt::Number g)
	Method to request the constraint values. More...

virtual bool	eval_grad_f (Ipopt::Index n, const Ipopt::Number x, bool new_x, Ipopt::Number grad_f)
	Method to request the gradient of the objective function. More...

virtual bool	eval_h (Ipopt::Index n, const Ipopt::Number x, bool new_x, Ipopt::Number obj_factor, Ipopt::Index m, const Ipopt::Number lambda, bool new_lambda, Ipopt::Index nele_hess, Ipopt::Index iRow, Ipopt::Index jCol, Ipopt::Number *values)
	Method to request either the sparsity structure or the values of the Hessian of the Lagrangian. More...

virtual bool	eval_jac_g (Ipopt::Index n, const Ipopt::Number x, bool new_x, Ipopt::Index m, Ipopt::Index nele_jac, Ipopt::Index iRow, Ipopt::Index jCol, Ipopt::Number values)
	Method to request either the sparsity structure or the values of the Jacobian of the constraints. More...

virtual void	finalize_solution (Ipopt::SolverReturn status, Ipopt::Index n, const Ipopt::Number x, const Ipopt::Number z_L, const Ipopt::Number z_U, Ipopt::Index m, const Ipopt::Number g, const Ipopt::Number lambda, Ipopt::Number obj_value, const Ipopt::IpoptData ip_data, Ipopt::IpoptCalculatedQuantities *ip_cq)
	This method is called when the algorithm has finished (successfully or not) so the TNLP can digest the outcome, e.g., store/write the solution, if any. More...

virtual bool	get_bounds_info (Ipopt::Index n, Ipopt::Number x_l, Ipopt::Number x_u, Ipopt::Index m, Ipopt::Number g_l, Ipopt::Number g_u)
	Method to request bounds on the variables and constraints. T. More...

double	get_cost () const

std::size_t	get_nconst () const
	Return the total number of constraints in the NLP.

virtual bool	get_nlp_info (Ipopt::Index &n, Ipopt::Index &m, Ipopt::Index &nnz_jac_g, Ipopt::Index &nnz_h_lag, IndexStyleEnum &index_style)
	Methods to gather information about the NLP. More...

std::size_t	get_nvar () const
	Return the total number of optimization variables (states and controls)

const boost::shared_ptr< crocoddyl::ShootingProblem > &	get_problem () const
	Return the crocoddyl::ShootingProblem to be solved.

virtual bool	get_starting_point (Ipopt::Index n, bool init_x, Ipopt::Number x, bool init_z, Ipopt::Number z_L, Ipopt::Number z_U, Ipopt::Index m, bool init_lambda, Ipopt::Number lambda)
	Method to request the starting point before iterating. More...

const std::vector< Eigen::VectorXd > &	get_us () const
	Return the control vector.

const std::vector< Eigen::VectorXd > &	get_xs () const
	Return the state vector.

bool	intermediate_callback (Ipopt::AlgorithmMode mode, Ipopt::Index iter, Ipopt::Number obj_value, Ipopt::Number inf_pr, Ipopt::Number inf_du, Ipopt::Number mu, Ipopt::Number d_norm, Ipopt::Number regularization_size, Ipopt::Number alpha_du, Ipopt::Number alpha_pr, Ipopt::Index ls_trials, const Ipopt::IpoptData ip_data, Ipopt::IpoptCalculatedQuantities ip_cq)
	Intermediate Callback method for the user. More...

void	resizeData ()

void	set_us (const std::vector< Eigen::VectorXd > &us)
	Modify the control vector.

void	set_xs (const std::vector< Eigen::VectorXd > &xs)
	Modify the state vector.

Detailed Description

Class for interfacing a crocoddyl::ShootingProblem with IPOPT.

This class implements the pure virtual functions from Ipopt::TNLP to solve the optimal control problem in problem_ using a multiple shooting approach.

Ipopt considers its decision variables x to belong to the Euclidean space. However, Crocoddyl states could lie in a manifold. To ensure that the solution of Ipopt lies in the manifold of the state, we perform the optimization in the tangent space of a given initial state. Finally we retract the Ipopt solution to the manifold. That is:

\[ \begin{aligned} \mathbf{x}^* = \mathbf{x}^0 \oplus \mathbf{\Delta x}^* \end{aligned} \]

where \(\mathbf{x}^*\) is the final solution, \(\mathbf{x}^0\) is the initial guess and \(\mathbf{\Delta x}^*\) is the Ipopt solution in the tangent space of \(\mathbf{x}_0\). Due to this procedure, the computation of the cost function, the dynamic constraint as well as their corresponding derivatives should be properly modified.

The Ipopt decision vector is built as follows: \(x = [ \mathbf{\Delta x}_0^\top, \mathbf{u}_0^\top, \mathbf{\Delta x}_1^\top, \mathbf{u}_1^\top, \dots, \mathbf{\Delta x}_N^\top ]\)

Dynamic constraints are posed as: \((\mathbf{x}^0_{k+1} \oplus \mathbf{\Delta x}_{k+1}) \ominus \mathbf{f}(\mathbf{x}_{k}^0 \oplus \mathbf{\Delta x}_{k}, \mathbf{u}_k) = \mathbf{0}\)

Initial condition: \( \mathbf{x}(0) \ominus (\mathbf{x}_{k}^0 \oplus \mathbf{\Delta x}_{k}) = \mathbf{0}\)

Documentation of the methods has been extracted from Ipopt::TNLP.hpp file

See also: get_nlp_info(), get_bounds_info(), eval_f(), eval_g(), eval_grad_f(), eval_jac_g(), eval_h()

Definition at line 63 of file ipopt-iface.hpp.

Constructor & Destructor Documentation

◆ IpoptInterface()

EIGEN_MAKE_ALIGNED_OPERATOR_NEW IpoptInterface ( const boost::shared_ptr< crocoddyl::ShootingProblem > & problem )

Initialize the Ipopt interface.

Parameters

[in] problem Crocoddyl shooting problem

Member Function Documentation

◆ get_nlp_info()

bool get_nlp_info	(	Ipopt::Index &	n,
		Ipopt::Index &	m,
		Ipopt::Index &	nnz_jac_g,
		Ipopt::Index &	nnz_h_lag,
		IndexStyleEnum &	index_style
	)

virtual

Methods to gather information about the NLP.

Ipopt uses this information when allocating the arrays that it will later ask you to fill with values. Be careful in this method since incorrect values will cause memory bugs which may be very difficult to find.

Parameters

[out]	n	Storage for the number of variables \(x\)
[out]	m	Storage for the number of constraints \(g(x)\)
[out]	nnz_jac_g	Storage for the number of nonzero entries in the Jacobian
[out]	nnz_h_lag	Storage for the number of nonzero entries in the Hessian
[out]	index_style	Storage for the index style the numbering style used for row/col entries in the sparse matrix format

Definition at line 91 of file ipopt-iface.cpp.

◆ get_bounds_info()

bool get_bounds_info	(	Ipopt::Index	n,
		Ipopt::Number *	x_l,
		Ipopt::Number *	x_u,
		Ipopt::Index	m,
		Ipopt::Number *	g_l,
		Ipopt::Number *	g_u
	)

virtual

Method to request bounds on the variables and constraints. T.

Parameters

[in]	n	Number of variables \(x\) in the problem
[out]	x_l	Lower bounds \(x^L\) for the variables \(x\)
[out]	x_u	Upper bounds \(x^U\) for the variables \(x\)
[in]	m	Number of constraints \(g(x)\) in the problem
[out]	g_l	Lower bounds \(g^L\) for the constraints \(g(x)\)
[out]	g_u	Upper bounds \(g^U\) for the constraints \(g(x)\)

Returns: true if success, false otherwise.

The values of n and m that were specified in IpoptInterface::get_nlp_info are passed here for debug checking. Setting a lower bound to a value less than or equal to the value of the option nlp_lower_bound_inf will cause Ipopt to assume no lower bound. Likewise, specifying the upper bound above or equal to the value of the option nlp_upper_bound_inf will cause Ipopt to assume no upper bound. These options are set to -10¹⁹ and 10¹⁹, respectively, by default, but may be modified by changing these options.

Definition at line 139 of file ipopt-iface.cpp.

◆ get_starting_point()

bool get_starting_point	(	Ipopt::Index	n,
		bool	init_x,
		Ipopt::Number *	x,
		bool	init_z,
		Ipopt::Number *	z_L,
		Ipopt::Number *	z_U,
		Ipopt::Index	m,
		bool	init_lambda,
		Ipopt::Number *	lambda
	)

virtual

Method to request the starting point before iterating.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	init_x	If true, this method must provide an initial value for \(x\)
[out]	x	Initial values for the primal variables \(x\)
[in]	init_z	If true, this method must provide an initial value for the bound multipliers \(z^L\) and \(z^U\)
[out]	z_L	Initial values for the bound multipliers \(z^L\)
[out]	z_U	Initial values for the bound multipliers \(z^U\)
[in]	m	Number of constraints \(g(x)\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	init_lambda	If true, this method must provide an initial value for the constraint multipliers \(\lambda\)
[out]	lambda	Initial values for the constraint multipliers, \(\lambda\)

Returns: true if success, false otherwise.

The boolean variables indicate whether the algorithm requires to have x, z_L/z_u, and lambda initialized, respectively. If, for some reason, the algorithm requires initializations that cannot be provided, false should be returned and Ipopt will stop. The default options only require initial values for the primal variables \(x\).

Note, that the initial values for bound multiplier components for absent bounds ( \(x^L_i=-\infty\) or \(x^U_i=\infty\)) are ignored.

Definition at line 192 of file ipopt-iface.cpp.

◆ eval_f()

bool eval_f	(	Ipopt::Index	n,
		const Ipopt::Number *	x,
		bool	new_x,
		Ipopt::Number &	obj_value
	)

virtual

Method to request the value of the objective function.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	Values for the primal variables \(x\) at which the objective function \(f(x)\) is to be evaluated
[in]	new_x	False if any evaluation method (`eval_*`) was previously called with the same values in x, true otherwise. This can be helpful when users have efficient implementations that calculate multiple outputs at once. Ipopt internally caches results from the TNLP and generally, this flag can be ignored.
[out]	obj_value	Storage for the value of the objective function \(f(x)\)

Returns: true if success, false otherwise.

Definition at line 240 of file ipopt-iface.cpp.

◆ eval_grad_f()

bool eval_grad_f	(	Ipopt::Index	n,
		const Ipopt::Number *	x,
		bool	new_x,
		Ipopt::Number *	grad_f
	)

virtual

Method to request the gradient of the objective function.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	Values for the primal variables \(x\) at which the gradient \(\nabla f(x)\) is to be evaluated
[in]	new_x	False if any evaluation method (`eval_*`) was previously called with the same values in x, true otherwise; see also `IpoptInterface::eval_f`
[out]	grad_f	Array to store values of the gradient of the objective function \(\nabla f(x)\). The gradient array is in the same order as the \(x\) variables (i.e., the gradient of the objective with respect to `x[2]` should be put in `grad_f[2]`).

Returns: true if success, false otherwise.

Definition at line 294 of file ipopt-iface.cpp.

◆ eval_g()

bool eval_g	(	Ipopt::Index	n,
		const Ipopt::Number *	x,
		bool	new_x,
		Ipopt::Index	m,
		Ipopt::Number *	g
	)

virtual

Method to request the constraint values.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	Values for the primal variables \(x\) at which the constraint functions \(g(x)\) are to be evaluated
[in]	new_x	False if any evaluation method (`eval_*`) was previously called with the same values in x, true otherwise; see also `IpoptInterface::eval_f`
[in]	m	Number of constraints \(g(x)\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[out]	g	Array to store constraint function values \(g(x)\), do not add or subtract the bound values \(g^L\) or \(g^U\).

Returns: true if success, false otherwise.

Definition at line 361 of file ipopt-iface.cpp.

◆ eval_jac_g()

bool eval_jac_g	(	Ipopt::Index	n,
		const Ipopt::Number *	x,
		bool	new_x,
		Ipopt::Index	m,
		Ipopt::Index	nele_jac,
		Ipopt::Index *	iRow,
		Ipopt::Index *	jCol,
		Ipopt::Number *	values
	)

virtual

Method to request either the sparsity structure or the values of the Jacobian of the constraints.

The Jacobian is the matrix of derivatives where the derivative of constraint function \(g_i\) with respect to variable \(x_j\) is placed in row \(i\) and column \(j\). See TRIPLET for a discussion of the sparse matrix format used in this method.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	First call: NULL; later calls: the values for the primal variables \(x\) at which the constraint Jacobian \(\nabla g(x)^T\) is to be evaluated
[in]	new_x	False if any evaluation method (`eval_*`) was previously called with the same values in x, true otherwise; see also `IpoptInterface::eval_f`
[in]	m	Number of constraints \(g(x)\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	nele_jac	Number of nonzero elements in the Jacobian; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[out]	iRow	First call: array of length `nele_jac` to store the row indices of entries in the Jacobian f the constraints; later calls: NULL
[out]	jCol	First call: array of length `nele_jac` to store the column indices of entries in the acobian of the constraints; later calls: NULL
[out]	values	First call: NULL; later calls: array of length nele_jac to store the values of the entries in the Jacobian of the constraints

Returns: true if success, false otherwise.

Note: The arrays iRow and jCol only need to be filled once. If the iRow and jCol arguments are not NULL (first call to this function), then Ipopt expects that the sparsity structure of the Jacobian (the row and column indices only) are written into iRow and jCol. At this call, the arguments x and values will be NULL. If the arguments x and values are not NULL, then Ipopt expects that the value of the Jacobian as calculated from array x is stored in array values (using the same order as used when specifying the sparsity structure). At this call, the arguments iRow and jCol will be NULL.

Definition at line 426 of file ipopt-iface.cpp.

◆ eval_h()

bool eval_h	(	Ipopt::Index	n,
		const Ipopt::Number *	x,
		bool	new_x,
		Ipopt::Number	obj_factor,
		Ipopt::Index	m,
		const Ipopt::Number *	lambda,
		bool	new_lambda,
		Ipopt::Index	nele_hess,
		Ipopt::Index *	iRow,
		Ipopt::Index *	jCol,
		Ipopt::Number *	values
	)

virtual

Method to request either the sparsity structure or the values of the Hessian of the Lagrangian.

The Hessian matrix that Ipopt uses is

\[ \sigma_f \nabla^2 f(x_k) + \sum_{i=1}^m\lambda_i\nabla^2 g_i(x_k) \]

for the given values for \(x\), \(\sigma_f\), and \(\lambda\). See TRIPLET for a discussion of the sparse matrix format used in this method.

Parameters

[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	First call: NULL; later calls: the values for the primal variables \(x\) at which the Hessian is to be evaluated
[in]	new_x	False if any evaluation method (`eval_*`) was previously called with the same values in x, true otherwise; see also IpoptInterface::eval_f
[in]	obj_factor	Factor \(\sigma_f\) in front of the objective term in the Hessian
[in]	m	Number of constraints \(g(x)\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	lambda	Values for the constraint multipliers \(\lambda\) at which the Hessian is to be evaluated
[in]	new_lambda	False if any evaluation method was previously called with the same values in lambda, true otherwise
[in]	nele_hess	Number of nonzero elements in the Hessian; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[out]	iRow	First call: array of length nele_hess to store the row indices of entries in the Hessian; later calls: NULL
[out]	jCol	First call: array of length nele_hess to store the column indices of entries in the Hessian; later calls: NULL
[out]	values	First call: NULL; later calls: array of length nele_hess to store the values of the entries in the Hessian

Returns: true if success, false otherwise.

Note: The arrays iRow and jCol only need to be filled once. If the iRow and jCol arguments are not NULL (first call to this function), then Ipopt expects that the sparsity structure of the Hessian (the row and column indices only) are written into iRow and jCol. At this call, the arguments x, lambda, and values will be NULL. If the arguments x, lambda, and values are not NULL, then Ipopt expects that the value of the Hessian as calculated from arrays x and lambda are stored in array values (using the same order as used when specifying the sparsity structure). At this call, the arguments iRow and jCol will be NULL.

Attention: As this matrix is symmetric, Ipopt expects that only the lower diagonal entries are specified.

A default implementation is provided, in case the user wants to set quasi-Newton approximations to estimate the second derivatives and doesn't not need to implement this method.

Definition at line 568 of file ipopt-iface.cpp.

◆ finalize_solution()

void finalize_solution	(	Ipopt::SolverReturn	status,
		Ipopt::Index	n,
		const Ipopt::Number *	x,
		const Ipopt::Number *	z_L,
		const Ipopt::Number *	z_U,
		Ipopt::Index	m,
		const Ipopt::Number *	g,
		const Ipopt::Number *	lambda,
		Ipopt::Number	obj_value,
		const Ipopt::IpoptData *	ip_data,
		Ipopt::IpoptCalculatedQuantities *	ip_cq
	)

virtual

This method is called when the algorithm has finished (successfully or not) so the TNLP can digest the outcome, e.g., store/write the solution, if any.

Parameters

[in]	status	gives the status of the algorithm SUCCESS: Algorithm terminated successfully at a locally optimal point, satisfying the convergence tolerances (can be specified by options). MAXITER_EXCEEDED: Maximum number of iterations exceeded (can be specified by an option). CPUTIME_EXCEEDED: Maximum number of CPU seconds exceeded (can be specified by an option). STOP_AT_TINY_STEP: Algorithm proceeds with very little progress. STOP_AT_ACCEPTABLE_POINT: Algorithm stopped at a point that was converged, not to "desired" tolerances, but to "acceptable" tolerances (see the acceptable-... options). LOCAL_INFEASIBILITY: Algorithm converged to a point of local infeasibility. Problem may be infeasible. USER_REQUESTED_STOP: The user call-back function IpoptInterface::intermediate_callback returned false, i.e., the user code requested a premature termination of the optimization. DIVERGING_ITERATES: It seems that the iterates diverge. RESTORATION_FAILURE: Restoration phase failed, algorithm doesn't know how to proceed. ERROR_IN_STEP_COMPUTATION: An unrecoverable error occurred while Ipopt tried to compute the search direction. INVALID_NUMBER_DETECTED: Algorithm received an invalid number (such as NaN or Inf) from the NLP; see also option check_derivatives_for_nan_inf). INTERNAL_ERROR: An unknown internal error occurred.
[in]	n	Number of variables \(x\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	x	Final values for the primal variables
[in]	z_L	Final values for the lower bound multipliers
[in]	z_U	Final values for the upper bound multipliers
[in]	m	Number of constraints \(g(x)\) in the problem; it will have the same value that was specified in `IpoptInterface::get_nlp_info`
[in]	g	Final values of the constraint functions
[in]	lambda	Final values of the constraint multipliers
[in]	obj_value	Final value of the objective function
[in]	ip_data	Provided for expert users
[in]	ip_cq	Provided for expert users

Definition at line 718 of file ipopt-iface.cpp.

◆ intermediate_callback()

bool intermediate_callback	(	Ipopt::AlgorithmMode	mode,
		Ipopt::Index	iter,
		Ipopt::Number	obj_value,
		Ipopt::Number	inf_pr,
		Ipopt::Number	inf_du,
		Ipopt::Number	mu,
		Ipopt::Number	d_norm,
		Ipopt::Number	regularization_size,
		Ipopt::Number	alpha_du,
		Ipopt::Number	alpha_pr,
		Ipopt::Index	ls_trials,
		const Ipopt::IpoptData *	ip_data,
		Ipopt::IpoptCalculatedQuantities *	ip_cq
	)

Intermediate Callback method for the user.

This method is called once per iteration (during the convergence check), and can be used to obtain information about the optimization status while Ipopt solves the problem, and also to request a premature termination.

The information provided by the entities in the argument list correspond to what Ipopt prints in the iteration summary (see also OUTPUT). Further information can be obtained from the ip_data and ip_cq objects. The current iterate and violations of feasibility and optimality can be accessed via the methods IpoptInterface::get_curr_iterate() and IpoptInterface::get_curr_violations(). These methods translate values for the internal representation of the problem from ip_data and ip_cq objects into the TNLP representation.

Returns: If this method returns false, Ipopt will terminate with the User_Requested_Stop status.

It is not required to implement (overload) this method. The default implementation always returns true.

Definition at line 750 of file ipopt-iface.cpp.

◆ createData()

boost::shared_ptr< IpoptInterfaceData > createData	(	const std::size_t	nx,
		const std::size_t	ndx,
		const std::size_t	nu
	)

Create the data structure to store temporary computations.

Returns: the IpoptInterface Data

Definition at line 761 of file ipopt-iface.cpp.

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/ipopt/ipopt-iface.hpp
/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/src/core/solvers/ipopt/ipopt-iface.cpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ IpoptInterface()

Member Function Documentation

◆ get_nlp_info()

◆ get_bounds_info()

◆ get_starting_point()

◆ eval_f()

◆ eval_grad_f()

◆ eval_g()

◆ eval_jac_g()

◆ eval_h()

◆ finalize_solution()

◆ intermediate_callback()

◆ createData()