Base class for boundary control problems with Neumann boundary conditions, as formulated by Hans Mittelmann as Examples 5-8 in "Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints. More...

#include <MittelmannBndryCntrlNeum.hpp>

Inheritance diagram for MittelmannBndryCntrlNeumBase:

Public Member Functions
	MittelmannBndryCntrlNeumBase ()
	Constructor. More...

virtual	~MittelmannBndryCntrlNeumBase ()
	Default destructor. More...

virtual bool	get_scaling_parameters (Number &obj_scaling, bool &use_x_scaling, Index n, Number x_scaling, bool &use_g_scaling, Index m, Number g_scaling)
	Method for returning scaling parameters. More...

Overloaded from TNLP
virtual bool	get_nlp_info (Index &n, Index &m, Index &nnz_jac_g, Index &nnz_h_lag, IndexStyleEnum &index_style)
	Method to return some info about the nlp. More...

virtual bool	get_bounds_info (Index n, Number x_l, Number x_u, Index m, Number g_l, Number g_u)
	Method to return the bounds for my problem. More...

virtual bool	get_starting_point (Index n, bool init_x, Number x, bool init_z, Number z_L, Number z_U, Index m, bool init_lambda, Number lambda)
	Method to return the starting point for the algorithm. More...

virtual bool	eval_f (Index n, const Number *x, bool new_x, Number &obj_value)
	Method to return the objective value. More...

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

virtual bool	eval_g (Index n, const Number x, bool new_x, Index m, Number g)
	Method to return the constraint residuals. More...

virtual bool	eval_jac_g (Index n, const Number x, bool new_x, Index m, Index nele_jac, Index iRow, Index jCol, Number values)
	Method to return: 1) The structure of the jacobian (if "values" is NULL) 2) The values of the jacobian (if "values" is not NULL) More...

virtual bool	eval_h (Index n, const Number x, bool new_x, Number obj_factor, Index m, const Number lambda, bool new_lambda, Index nele_hess, Index iRow, Index jCol, Number *values)
	Method to return: 1) The structure of the hessian of the lagrangian (if "values" is NULL) 2) The values of the hessian of the lagrangian (if "values" is not NULL) More...

Solution Methods
virtual void	finalize_solution (SolverReturn status, Index n, const Number x, const Number z_L, const Number z_U, Index m, const Number g, const Number lambda, Number obj_value, const IpoptData ip_data, IpoptCalculatedQuantities *ip_cq)
	This method is called after the optimization, and could write an output file with the optimal profiles. More...

Public Member Functions inherited from RegisteredTNLP
virtual bool	InitializeProblem (Index N)=0
	Initialize internal parameters, where N is a parameter determining the problme size. More...

Public Member Functions inherited from Ipopt::TNLP
	DECLARE_STD_EXCEPTION (INVALID_TNLP)

	TNLP ()

virtual	~TNLP ()
	Default destructor. More...

virtual void	finalize_metadata (Index n, const StringMetaDataMapType &var_string_md, const IntegerMetaDataMapType &var_integer_md, const NumericMetaDataMapType &var_numeric_md, Index m, const StringMetaDataMapType &con_string_md, const IntegerMetaDataMapType &con_integer_md, const NumericMetaDataMapType &con_numeric_md)
	This method is called just before finalize_solution. More...

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

virtual Index	get_number_of_nonlinear_variables ()

virtual bool	get_list_of_nonlinear_variables (Index num_nonlin_vars, Index *pos_nonlin_vars)

virtual bool	get_var_con_metadata (Index n, StringMetaDataMapType &var_string_md, IntegerMetaDataMapType &var_integer_md, NumericMetaDataMapType &var_numeric_md, Index m, StringMetaDataMapType &con_string_md, IntegerMetaDataMapType &con_integer_md, NumericMetaDataMapType &con_numeric_md)
	overload this method to return any meta data for the variables and the constraints More...

virtual bool	get_variables_linearity (Index n, LinearityType *var_types)
	overload this method to return the variables linearity (TNLP::LINEAR or TNLP::NON_LINEAR). More...

virtual bool	get_constraints_linearity (Index m, LinearityType *const_types)
	overload this method to return the constraint linearity. More...

virtual bool	get_warm_start_iterate (IteratesVector &warm_start_iterate)
	overload this method to provide an Ipopt iterate (already in the form Ipopt requires it internally) for a warm start. More...

Public Member Functions inherited from Ipopt::ReferencedObject
	ReferencedObject ()

virtual	~ReferencedObject ()

Index	ReferenceCount () const

void	AddRef (const Referencer *referencer) const

void	ReleaseRef (const Referencer *referencer) const

Protected Member Functions
void	SetBaseParameters (Index N, Number alpha, Number lb_y, Number ub_y, Number lb_u, Number ub_u, Number u_init)
	Method for setting the internal parameters that define the problem. More...

Functions that defines a particular instance.
virtual Number	y_d_cont (Number x1, Number x2) const =0
	Target profile function for y (and initial guess function) More...

virtual Number	d_cont (Number x1, Number x2, Number y) const =0
	Forcing function for the elliptic equation. More...

virtual Number	d_cont_dy (Number x1, Number x2, Number y) const =0
	First partial derivative of forcing function w.r.t. More...

virtual Number	d_cont_dydy (Number x1, Number x2, Number y) const =0
	Second partial derivative of forcing function w.r.t. More...

virtual bool	d_cont_dydy_alwayszero () const =0
	returns true if second partial derivative of d_cont w.r.t. More...

virtual Number	b_cont (Number x1, Number x2, Number y, Number u) const =0
	Function in Neuman boundary condition. More...

virtual Number	b_cont_dy (Number x1, Number x2, Number y, Number u) const =0
	First partial derivative of b_cont w.r.t. More...

virtual Number	b_cont_du (Number x1, Number x2, Number y, Number u) const =0
	First partial derivative of b_cont w.r.t. More...

virtual Number	b_cont_dydy (Number x1, Number x2, Number y, Number u) const =0
	Second partial derivative of b_cont w.r.t. More...

virtual bool	b_cont_dydy_alwayszero () const =0
	returns true if second partial derivative of b_cont w.r.t. More...

Private Member Functions
Methods to block default compiler methods.
The compiler automatically generates the following three methods. Since the default compiler implementation is generally not what you want (for all but the most simple classes), we usually put the declarations of these methods in the private section and never implement them. This prevents the compiler from implementing an incorrect "default" behavior without us knowing. (See Scott Meyers book, "Effective C++")
	MittelmannBndryCntrlNeumBase (const MittelmannBndryCntrlNeumBase &)

MittelmannBndryCntrlNeumBase &	operator= (const MittelmannBndryCntrlNeumBase &)

Auxilliary methods
Index	y_index (Index i, Index j) const
	Translation of mesh point indices to NLP variable indices for y(x_ij) More...

Index	u0j_index (Index j) const
	Translation of mesh point indices to NLP variable indices for u(x_ij) on {0} x (0,1) boudnary. More...

Index	u1j_index (Index j) const
	Translation of mesh point indices to NLP variable indices for u(x_ij) on {1} x (0,1) boudnary. More...

Index	ui0_index (Index j) const
	Translation of mesh point indices to NLP variable indices for u(x_ij) on (0,1) x {0} boudnary. More...

Index	ui1_index (Index j) const
	Translation of mesh point indices to NLP variable indices for u(x_ij) on (0,1) x {1} boudnary. More...

Number	x1_grid (Index i) const
	Compute the grid coordinate for given index in x1 direction. More...

Number	x2_grid (Index j) const
	Compute the grid coordinate for given index in x2 direction. More...

Private Attributes
Problem specification
Index	N_
	Number of mesh points in one dimension (excluding boundary) More...

Number	h_
	Step size. More...

Number	hh_
	h_ squaredd More...

Number	lb_y_
	overall lower bound on y More...

Number	ub_y_
	overall upper bound on y More...

Number	lb_u_
	overall lower bound on u More...

Number	ub_u_
	overall upper bound on u More...

Number	u_init_
	Initial value for the constrols u. More...

Number	alpha_
	Weighting parameter for the control target deviation functional in the objective. More...

Number *	y_d_
	Array for the target profile for y. More...

Additional Inherited Members
Public Types inherited from Ipopt::TNLP
enum	LinearityType { LINEAR, NON_LINEAR }
	Type of the constraints. More...

enum	IndexStyleEnum { C_STYLE =0, FORTRAN_STYLE =1 }
	overload this method to return the number of variables and constraints, and the number of non-zeros in the jacobian and the hessian. More...

typedef std::map< std::string, std::vector< std::string > >	StringMetaDataMapType

typedef std::map< std::string, std::vector< Index > >	IntegerMetaDataMapType

typedef std::map< std::string, std::vector< Number > >	NumericMetaDataMapType

Detailed Description

Base class for boundary control problems with Neumann boundary conditions, as formulated by Hans Mittelmann as Examples 5-8 in "Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints.

Part 1: Boundary Control"

Definition at line 49 of file MittelmannBndryCntrlNeum.hpp.

Constructor & Destructor Documentation

MittelmannBndryCntrlNeumBase::MittelmannBndryCntrlNeumBase ( )

Constructor.

N is the number of mesh points in one dimension (excluding boundary).

virtual MittelmannBndryCntrlNeumBase::~MittelmannBndryCntrlNeumBase ( )

virtual

Default destructor.

MittelmannBndryCntrlNeumBase::MittelmannBndryCntrlNeumBase ( const MittelmannBndryCntrlNeumBase & )

private

Member Function Documentation

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

virtual

Method to return some info about the nlp.

Implements Ipopt::TNLP.

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

virtual

Method to return the bounds for my problem.

Implements Ipopt::TNLP.

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

virtual

Method to return the starting point for the algorithm.

Implements Ipopt::TNLP.

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

virtual

Method to return the objective value.

Implements Ipopt::TNLP.

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

virtual

Method to return the gradient of the objective.

Implements Ipopt::TNLP.

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

virtual

Method to return the constraint residuals.

Implements Ipopt::TNLP.

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

virtual

Method to return: 1) The structure of the jacobian (if "values" is NULL) 2) The values of the jacobian (if "values" is not NULL)

Implements Ipopt::TNLP.

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

virtual

Method to return: 1) The structure of the hessian of the lagrangian (if "values" is NULL) 2) The values of the hessian of the lagrangian (if "values" is not NULL)

Reimplemented from Ipopt::TNLP.

virtual bool MittelmannBndryCntrlNeumBase::get_scaling_parameters	(	Number &	obj_scaling,
		bool &	use_x_scaling,
		Index	n,
		Number *	x_scaling,
		bool &	use_g_scaling,
		Index	m,
		Number *	g_scaling
	)

virtual

Method for returning scaling parameters.

Reimplemented from Ipopt::TNLP.

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

virtual

This method is called after the optimization, and could write an output file with the optimal profiles.

Implements Ipopt::TNLP.

void MittelmannBndryCntrlNeumBase::SetBaseParameters	(	Index	N,
		Number	alpha,
		Number	lb_y,
		Number	ub_y,
		Number	lb_u,
		Number	ub_u,
		Number	u_init
	)

protected

Method for setting the internal parameters that define the problem.

It must be called by the child class in its implementation of InitializeParameters.

virtual Number MittelmannBndryCntrlNeumBase::y_d_cont	(	Number	x1,
		Number	x2
	)		const

protectedpure virtual

Target profile function for y (and initial guess function)

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::d_cont	(	Number	x1,
		Number	x2,
		Number	y
	)		const

protectedpure virtual

Forcing function for the elliptic equation.

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::d_cont_dy	(	Number	x1,
		Number	x2,
		Number	y
	)		const

protectedpure virtual

First partial derivative of forcing function w.r.t.

y

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::d_cont_dydy	(	Number	x1,
		Number	x2,
		Number	y
	)		const

protectedpure virtual

Second partial derivative of forcing function w.r.t.

y,y

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual bool MittelmannBndryCntrlNeumBase::d_cont_dydy_alwayszero ( ) const

protectedpure virtual

returns true if second partial derivative of d_cont w.r.t.

y,y is always zero.

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::b_cont	(	Number	x1,
		Number	x2,
		Number	y,
		Number	u
	)		const

protectedpure virtual

Function in Neuman boundary condition.

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::b_cont_dy	(	Number	x1,
		Number	x2,
		Number	y,
		Number	u
	)		const

protectedpure virtual

First partial derivative of b_cont w.r.t.

y

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::b_cont_du	(	Number	x1,
		Number	x2,
		Number	y,
		Number	u
	)		const

protectedpure virtual

First partial derivative of b_cont w.r.t.

u

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual Number MittelmannBndryCntrlNeumBase::b_cont_dydy	(	Number	x1,
		Number	x2,
		Number	y,
		Number	u
	)		const

protectedpure virtual

Second partial derivative of b_cont w.r.t.

y,y

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

virtual bool MittelmannBndryCntrlNeumBase::b_cont_dydy_alwayszero ( ) const

protectedpure virtual

returns true if second partial derivative of b_cont w.r.t.

y,y is always zero.

Implemented in MittelmannBndryCntrlNeum4, MittelmannBndryCntrlNeum3, MittelmannBndryCntrlNeum2, and MittelmannBndryCntrlNeum1.

MittelmannBndryCntrlNeumBase& MittelmannBndryCntrlNeumBase::operator= ( const MittelmannBndryCntrlNeumBase & )

private

Index MittelmannBndryCntrlNeumBase::y_index	(	Index	i,
		Index	j
	)		const

inlineprivate

Translation of mesh point indices to NLP variable indices for y(x_ij)

Definition at line 201 of file MittelmannBndryCntrlNeum.hpp.

Index MittelmannBndryCntrlNeumBase::u0j_index ( Index j ) const

inlineprivate

Translation of mesh point indices to NLP variable indices for u(x_ij) on {0} x (0,1) boudnary.

Definition at line 207 of file MittelmannBndryCntrlNeum.hpp.

Index MittelmannBndryCntrlNeumBase::u1j_index ( Index j ) const

inlineprivate

Translation of mesh point indices to NLP variable indices for u(x_ij) on {1} x (0,1) boudnary.

Definition at line 213 of file MittelmannBndryCntrlNeum.hpp.

Index MittelmannBndryCntrlNeumBase::ui0_index ( Index j ) const

inlineprivate

Translation of mesh point indices to NLP variable indices for u(x_ij) on (0,1) x {0} boudnary.

Definition at line 219 of file MittelmannBndryCntrlNeum.hpp.

Index MittelmannBndryCntrlNeumBase::ui1_index ( Index j ) const

inlineprivate

Translation of mesh point indices to NLP variable indices for u(x_ij) on (0,1) x {1} boudnary.

Definition at line 225 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::x1_grid ( Index i ) const

inlineprivate

Compute the grid coordinate for given index in x1 direction.

Definition at line 230 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::x2_grid ( Index j ) const

inlineprivate

Compute the grid coordinate for given index in x2 direction.

Definition at line 235 of file MittelmannBndryCntrlNeum.hpp.

Member Data Documentation

Index MittelmannBndryCntrlNeumBase::N_

private

Number of mesh points in one dimension (excluding boundary)

Definition at line 175 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::h_

private

Step size.

Definition at line 177 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::hh_

private

h_ squaredd

Definition at line 179 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::lb_y_

private

overall lower bound on y

Definition at line 181 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::ub_y_

private

overall upper bound on y

Definition at line 183 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::lb_u_

private

overall lower bound on u

Definition at line 185 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::ub_u_

private

overall upper bound on u

Definition at line 187 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::u_init_

private

Initial value for the constrols u.

Definition at line 189 of file MittelmannBndryCntrlNeum.hpp.

Number MittelmannBndryCntrlNeumBase::alpha_

private

Weighting parameter for the control target deviation functional in the objective.

Definition at line 192 of file MittelmannBndryCntrlNeum.hpp.

Number* MittelmannBndryCntrlNeumBase::y_d_

private

Array for the target profile for y.

Definition at line 194 of file MittelmannBndryCntrlNeum.hpp.

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

examples/ScalableProblems/MittelmannBndryCntrlNeum.hpp

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation