# MittelmannBndryCntrlDiriBase3D 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.hpp>`

Inheritance diagram for MittelmannBndryCntrlDiriBase3D:
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List of all members.

## Public Member Functions
| MittelmannBndryCntrlDiriBase3D ()
| Constructor.
virtual | ~MittelmannBndryCntrlDiriBase3D ()
| 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 (const MittelmannBndryCntrlDiriBase3D &)
MittelmannBndryCntrlDiriBase3D & | operator= (const MittelmannBndryCntrlDiriBase3D &)
| 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 53 of file MittelmannBndryCntrlDiri3D.hpp.

## Constructor & Destructor Documentation

MittelmannBndryCntrlDiriBase3D::MittelmannBndryCntrlDiriBase3D | ( |  | ) |

Constructor.

virtual MittelmannBndryCntrlDiriBase3D::~MittelmannBndryCntrlDiriBase3D | ( |  | ) | `[virtual]`

Default destructor.

MittelmannBndryCntrlDiriBase3D::MittelmannBndryCntrlDiriBase3D | ( | const MittelmannBndryCntrlDiriBase3D & |  | ) | `[private]`

## Member Function Documentation

virtual bool MittelmannBndryCntrlDiriBase3D::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::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::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::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::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::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::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::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::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::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::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::y_d_cont | ( | Number | x1,
|  | Number | x2,
|  | Number | x3 |
| ) |  |  | const`[protected, pure virtual]`

Target profile function for y.

Implemented in MittelmannBndryCntrlDiri3D.

MittelmannBndryCntrlDiriBase3D& MittelmannBndryCntrlDiriBase3D::operator= | ( | const MittelmannBndryCntrlDiriBase3D & |  | ) | `[private]`

Overloaded Equals Operator.

Reimplemented from Ipopt::TNLP.

Reimplemented in MittelmannBndryCntrlDiri3D.

Index MittelmannBndryCntrlDiriBase3D::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 186 of file MittelmannBndryCntrlDiri3D.hpp.

Index MittelmannBndryCntrlDiriBase3D::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 192 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::x1_grid | ( | Index | i | ) | const`[inline, private]`

Compute the grid coordinate for given index in x1 direction.

Definition at line 197 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::x2_grid | ( | Index | i | ) | const`[inline, private]`

Compute the grid coordinate for given index in x2 direction.

Definition at line 202 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::x3_grid | ( | Index | i | ) | const`[inline, private]`

Compute the grid coordinate for given index in x3 direction.

Definition at line 207 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenObj | ( | Number | t | ) | const`[inline, private]`

value of penalty function term

Definition at line 212 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenObj_1 | ( | Number | t | ) | const`[inline, private]`

first derivative of penalty function term

Definition at line 229 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenObj_2 | ( | Number | t | ) | const`[inline, private]`

second derivative of penalty function term

Definition at line 246 of file MittelmannBndryCntrlDiri3D.hpp.

## Member Data Documentation

Index MittelmannBndryCntrlDiriBase3D::N_`[private]`

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

Definition at line 158 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::h_`[private]`

Step size.

Definition at line 160 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::hh_`[private]`

h_ squared

Definition at line 162 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::hhh_`[private]`

h_ to the third power

Definition at line 164 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::lb_y_`[private]`

overall lower bound on y

Definition at line 166 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::ub_y_`[private]`

overall upper bound on y

Definition at line 168 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::lb_u_`[private]`

overall lower bound on u

Definition at line 170 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::ub_u_`[private]`

overall upper bound on u

Definition at line 172 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::d_const_`[private]`

Constant value of d appearing in elliptical equation.

Definition at line 174 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::alpha_`[private]`

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

Definition at line 177 of file MittelmannBndryCntrlDiri3D.hpp.

Number* MittelmannBndryCntrlDiriBase3D::y_d_`[private]`

Array for the target profile for y.

Definition at line 179 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::B_`[private]`

Definition at line 265 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::C_`[private]`

Definition at line 266 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenA_`[private]`

Definition at line 267 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenB_`[private]`

Definition at line 268 of file MittelmannBndryCntrlDiri3D.hpp.

Number MittelmannBndryCntrlDiriBase3D::PenC_`[private]`

Definition at line 269 of file MittelmannBndryCntrlDiri3D.hpp.

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

- examples/ScalableProblems/MittelmannBndryCntrlDiri3D.hpp

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