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MittelmannBndryCntrlNeumBase Class Referenceabstract

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 &)
 
MittelmannBndryCntrlNeumBaseoperator= (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...
 
Numbery_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: