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# MittelmannBndryCntrlDiriBase 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 <MittelmannBndryCntrlDiri.hpp>`

Inheritance diagram for MittelmannBndryCntrlDiriBase:

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Collaboration diagram for MittelmannBndryCntrlDiriBase:

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List of all members.

## Public Member Functions
| MittelmannBndryCntrlDiriBase ()
| Constructor.
virtual | ~MittelmannBndryCntrlDiriBase ()
| 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_value)
| 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)
| 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) 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++")
| MittelmannBndryCntrlDiriBase (const MittelmannBndryCntrlDiriBase &)
MittelmannBndryCntrlDiriBase & | operator= (const MittelmannBndryCntrlDiriBase &)
Auxilliary methods
Index | y_index (Index i, Index j) const
| Translation of mesh point indices to NLP variable indices for y(x_ij).
Index | pde_index (Index i, Index j) 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.
## Private Attributes
Problem specification
Index | N_
| Number of mesh points in one dimension (excluding boundary).
Number | h_
| Step size.
Number | hh_
| h_ squaredd
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.

## 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 36 of file MittelmannBndryCntrlDiri.hpp.

## Constructor & Destructor Documentation

MittelmannBndryCntrlDiriBase::MittelmannBndryCntrlDiriBase | ( |  | ) |

Constructor.

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

Default destructor.

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

## Member Function Documentation

virtual bool MittelmannBndryCntrlDiriBase::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.

virtual bool MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 MittelmannBndryCntrlDiriBase::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 |
| ) |  |  | `[virtual]`

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

Implements Ipopt::TNLP.

void MittelmannBndryCntrlDiriBase::SetBaseParameters | ( | Index | N,
|  | Number | alpha,
|  | Number | lb_y,
|  | Number | ub_y,
|  | Number | lb_u,
|  | Number | ub_u,
|  | Number | d_const |
| ) |  |  | `[protected]`

Method for setting the internal parameters that define the problem.

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

Referenced by MittelmannBndryCntrlDiri4::InitializeProblem(), MittelmannBndryCntrlDiri3::InitializeProblem(), MittelmannBndryCntrlDiri2::InitializeProblem(), and MittelmannBndryCntrlDiri1::InitializeProblem().

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

Target profile function for y.

Implemented in MittelmannBndryCntrlDiri1, MittelmannBndryCntrlDiri2, MittelmannBndryCntrlDiri3, and MittelmannBndryCntrlDiri4.

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

Index MittelmannBndryCntrlDiriBase::y_index | ( | Index | i,
|  | Index | j |
| ) |  |  | const`[inline, private]`

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

Definition at line 165 of file MittelmannBndryCntrlDiri.hpp.

References N_.

Index MittelmannBndryCntrlDiriBase::pde_index | ( | Index | i,
|  | Index | j |
| ) |  |  | const`[inline, private]`

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

Definition at line 171 of file MittelmannBndryCntrlDiri.hpp.

References N_.

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

Compute the grid coordinate for given index in x1 direction.

Definition at line 176 of file MittelmannBndryCntrlDiri.hpp.

References h_.

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

Compute the grid coordinate for given index in x2 direction.

Definition at line 181 of file MittelmannBndryCntrlDiri.hpp.

References h_.

## Member Data Documentation

Index MittelmannBndryCntrlDiriBase::N_`[private]`

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

Definition at line 139 of file MittelmannBndryCntrlDiri.hpp.

Referenced by pde_index(), and y_index().

Number MittelmannBndryCntrlDiriBase::h_`[private]`

Step size.

Definition at line 141 of file MittelmannBndryCntrlDiri.hpp.

Referenced by x1_grid(), and x2_grid().

Number MittelmannBndryCntrlDiriBase::hh_`[private]`

h_ squaredd

Definition at line 143 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::lb_y_`[private]`

overall lower bound on y

Definition at line 145 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::ub_y_`[private]`

overall upper bound on y

Definition at line 147 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::lb_u_`[private]`

overall lower bound on u

Definition at line 149 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::ub_u_`[private]`

overall upper bound on u

Definition at line 151 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::d_const_`[private]`

Constant value of d appearing in elliptical equation.

Definition at line 153 of file MittelmannBndryCntrlDiri.hpp.

Number MittelmannBndryCntrlDiriBase::alpha_`[private]`

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

Definition at line 156 of file MittelmannBndryCntrlDiri.hpp.

Number* MittelmannBndryCntrlDiriBase::y_d_`[private]`

Array for the target profile for y.

Definition at line 158 of file MittelmannBndryCntrlDiri.hpp.

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

- /home/coin/SVN-release/Ipopt-3.2.1/Ipopt/examples/ScalableProblems/MittelmannBndryCntrlDiri.hpp