MittelmannBndryCntrlDiriBase3D_27 Class Reference

Base class for boundary control problems with Dirichlet boundary conditions, as formulated by Hans Mittelmann as Examples 1-4 in Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints. More...

#include <MittelmannBndryCntrlDiri3D_27.hpp>

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List of all members.

Public Member Functions

 MittelmannBndryCntrlDiriBase3D_27 ()
 Constructor.
virtual ~MittelmannBndryCntrlDiriBase3D_27 ()
 Default destructor.
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.
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.
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.
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.
virtual bool eval_f (Index n, const Number *x, bool new_x, Number &obj_value)
 Method to return the objective value.
virtual bool eval_grad_f (Index n, const Number *x, bool new_x, Number *grad_f)
 Method to return the gradient of the objective.
virtual bool eval_g (Index n, const Number *x, bool new_x, Index m, Number *g)
 Method to return the constraint residuals.
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).
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).
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_valu, const IpoptData *ip_data, IpoptCalculatedQuantities *ip_cq)
 This method is called after the optimization, and could write an output file with the optimal profiles.

Protected Member Functions

void SetBaseParameters (Index N, Number alpha, Number lb_y, Number ub_y, Number lb_u, Number ub_u, Number d_const, Number B, Number C)
 Method for setting the internal parameters that define the problem.
Functions that defines a particular instance.



virtual Number y_d_cont (Number x1, Number x2, Number x3) const =0
 Target profile function for y.

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++")



 MittelmannBndryCntrlDiriBase3D_27 (const MittelmannBndryCntrlDiriBase3D_27 &)
MittelmannBndryCntrlDiriBase3D_27 & operator= (const MittelmannBndryCntrlDiriBase3D_27 &)
 Overloaded Equals Operator.
Auxilliary methods



Index y_index (Index i, Index j, Index k) const
 Translation of mesh point indices to NLP variable indices for y(x_ijk).
Index pde_index (Index i, Index j, Index k) const
 Translation of interior mesh point indices to the corresponding PDE constraint number.
Number x1_grid (Index i) const
 Compute the grid coordinate for given index in x1 direction.
Number x2_grid (Index i) const
 Compute the grid coordinate for given index in x2 direction.
Number x3_grid (Index i) const
 Compute the grid coordinate for given index in x3 direction.
Number PenObj (Number t) const
 value of penalty function term
Number PenObj_1 (Number t) const
 first derivative of penalty function term
Number PenObj_2 (Number t) const
 second derivative of penalty function term

Private Attributes

Problem specification



Index N_
 Number of mesh points in one dimension (excluding boundary).
Number h_
 Step size.
Number hh_
 h_ squared
Number hhh_
 h_ to the third power
Number lb_y_
 overall lower bound on y
Number ub_y_
 overall upper bound on y
Number lb_u_
 overall lower bound on u
Number ub_u_
 overall upper bound on u
Number d_const_
 Constant value of d appearing in elliptical equation.
Number alpha_
 Weighting parameter for the control target deviation functional in the objective.
Number * y_d_
 Array for the target profile for y.
Data for penalty function term



Number B_
Number C_
Number PenA_
Number PenB_
Number PenC_

Detailed Description

Base class for boundary control problems with Dirichlet boundary conditions, as formulated by Hans Mittelmann as Examples 1-4 in Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints.

Part 2: Boundary Control

Here, the control variables are identical to the values of y on the boundary, and therefore we don't need any explicit optimization variables for u.

Definition at line 37 of file MittelmannBndryCntrlDiri3D_27.hpp.

Constructor & Destructor Documentation

MittelmannBndryCntrlDiriBase3D_27::MittelmannBndryCntrlDiriBase3D_27 (  ) 

Constructor.

virtual MittelmannBndryCntrlDiriBase3D_27::~MittelmannBndryCntrlDiriBase3D_27 (  )  [virtual]

Default destructor.

MittelmannBndryCntrlDiriBase3D_27::MittelmannBndryCntrlDiriBase3D_27 ( const MittelmannBndryCntrlDiriBase3D_27 &   )  [private]

Member Function Documentation

virtual bool MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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 MittelmannBndryCntrlDiriBase3D_27::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_valu,
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 MittelmannBndryCntrlDiriBase3D_27::SetBaseParameters ( Index  N,
Number  alpha,
Number  lb_y,
Number  ub_y,
Number  lb_u,
Number  ub_u,
Number  d_const,
Number  B,
Number  C 
) [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 MittelmannBndryCntrlDiriBase3D_27::y_d_cont ( Number  x1,
Number  x2,
Number  x3 
) const [protected, pure virtual]

Target profile function for y.

Implemented in MittelmannBndryCntrlDiri3D_27, and MittelmannBndryCntrlDiri3D_27BT.

MittelmannBndryCntrlDiriBase3D_27& MittelmannBndryCntrlDiriBase3D_27::operator= ( const MittelmannBndryCntrlDiriBase3D_27 &   )  [private]

Overloaded Equals Operator.

Reimplemented from Ipopt::TNLP.

Reimplemented in MittelmannBndryCntrlDiri3D_27, and MittelmannBndryCntrlDiri3D_27BT.

Index MittelmannBndryCntrlDiriBase3D_27::y_index ( Index  i,
Index  j,
Index  k 
) const [inline, private]

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

Definition at line 170 of file MittelmannBndryCntrlDiri3D_27.hpp.

Index MittelmannBndryCntrlDiriBase3D_27::pde_index ( Index  i,
Index  j,
Index  k 
) const [inline, private]

Translation of interior mesh point indices to the corresponding PDE constraint number.

Definition at line 176 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::x1_grid ( Index  i  )  const [inline, private]

Compute the grid coordinate for given index in x1 direction.

Definition at line 181 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::x2_grid ( Index  i  )  const [inline, private]

Compute the grid coordinate for given index in x2 direction.

Definition at line 186 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::x3_grid ( Index  i  )  const [inline, private]

Compute the grid coordinate for given index in x3 direction.

Definition at line 191 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenObj ( Number  t  )  const [inline, private]

value of penalty function term

Definition at line 196 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenObj_1 ( Number  t  )  const [inline, private]

first derivative of penalty function term

Definition at line 215 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenObj_2 ( Number  t  )  const [inline, private]

second derivative of penalty function term

Definition at line 234 of file MittelmannBndryCntrlDiri3D_27.hpp.

Member Data Documentation

Index MittelmannBndryCntrlDiriBase3D_27::N_ [private]

Number of mesh points in one dimension (excluding boundary).

Definition at line 142 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::h_ [private]

Step size.

Definition at line 144 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::hh_ [private]

h_ squared

Definition at line 146 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::hhh_ [private]

h_ to the third power

Definition at line 148 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::lb_y_ [private]

overall lower bound on y

Definition at line 150 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::ub_y_ [private]

overall upper bound on y

Definition at line 152 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::lb_u_ [private]

overall lower bound on u

Definition at line 154 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::ub_u_ [private]

overall upper bound on u

Definition at line 156 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::d_const_ [private]

Constant value of d appearing in elliptical equation.

Definition at line 158 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::alpha_ [private]

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

Definition at line 161 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number* MittelmannBndryCntrlDiriBase3D_27::y_d_ [private]

Array for the target profile for y.

Definition at line 163 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::B_ [private]

Definition at line 255 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::C_ [private]

Definition at line 256 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenA_ [private]

Definition at line 257 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenB_ [private]

Definition at line 258 of file MittelmannBndryCntrlDiri3D_27.hpp.

Number MittelmannBndryCntrlDiriBase3D_27::PenC_ [private]

Definition at line 259 of file MittelmannBndryCntrlDiri3D_27.hpp.

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