# MittelmannDistCntrlNeumABase Class Reference

Base class for distributed control problems with homogeneous Neumann boundary conditions, as formulated by Hans Mittelmann as Examples 4-6 in Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints. More...

`#include <MittelmannDistCntrlNeumA.hpp>`

Inheritance diagram for MittelmannDistCntrlNeumABase:
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List of all members.

## Public Member Functions
| MittelmannDistCntrlNeumABase ()
| Constructor.
virtual | ~MittelmannDistCntrlNeumABase ()
| 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, 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 lb_y, Number ub_y, Number lb_u, Number ub_u, Number b_0j, Number b_1j, Number b_i0, Number b_i1, Number u_init)
| 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 (and initial guess function).
virtual Number | fint_cont (Number x1, Number x2, Number y, Number u) const =0
| Integrant in objective function.
virtual Number | fint_cont_dy (Number x1, Number x2, Number y, Number u) const =0
| First partial derivative of fint_cont w.r.t.
virtual Number | fint_cont_du (Number x1, Number x2, Number y, Number u) const =0
| First partial derivative of fint_cont w.r.t.
virtual Number | fint_cont_dydy (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of fint_cont w.r.t.
virtual bool | fint_cont_dydy_alwayszero () const =0
| returns true if second partial derivative of fint_cont w.r.t.
virtual Number | fint_cont_dudu (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of fint_cont w.r.t.
virtual bool | fint_cont_dudu_alwayszero () const =0
| returns true if second partial derivative of fint_cont w.r.t.
virtual Number | fint_cont_dydu (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of fint_cont w.r.t.
virtual bool | fint_cont_dydu_alwayszero () const =0
| returns true if second partial derivative of fint_cont w.r.t.
virtual Number | d_cont (Number x1, Number x2, Number y, Number u) const =0
| Forcing function for the elliptic equation.
virtual Number | d_cont_dy (Number x1, Number x2, Number y, Number u) const =0
| First partial derivative of forcing function w.r.t.
virtual Number | d_cont_du (Number x1, Number x2, Number y, Number u) const =0
| First partial derivative of forcing function w.r.t.
virtual Number | d_cont_dydy (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of forcing function w.r.t.
virtual bool | d_cont_dydy_alwayszero () const =0
| returns true if second partial derivative of d_cont w.r.t.
virtual Number | d_cont_dudu (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of forcing function w.r.t.
virtual bool | d_cont_dudu_alwayszero () const =0
| returns true if second partial derivative of d_cont w.r.t.
virtual Number | d_cont_dydu (Number x1, Number x2, Number y, Number u) const =0
| Second partial derivative of forcing function w.r.t.
virtual bool | d_cont_dydu_alwayszero () const =0
| returns true if second partial derivative of d_cont w.r.t.
## 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++")
| MittelmannDistCntrlNeumABase (const MittelmannDistCntrlNeumABase &)
MittelmannDistCntrlNeumABase & | operator= (const MittelmannDistCntrlNeumABase &)
| Overloaded Equals Operator.
Auxilliary methods
Index | y_index (Index i, Index j) const
| Translation of mesh point indices to NLP variable indices for y(x_ij).
Index | u_index (Index i, Index j) const
| Translation of mesh point indices to NLP variable indices for u(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 | b_0j_
| Value of beta function (in Neumann boundary condition) for (0,x2) bounray.
Number | b_1j_
| Value of beta function (in Neumann boundary condition) for (1,x2) bounray.
Number | b_i0_
| Value of beta function (in Neumann boundary condition) for (x1,0) bounray.
Number | b_i1_
| Value of beta function (in Neumann boundary condition) for (x1,1) bounray.
Number | u_init_
| Initial value for the constrols u.
Number * | y_d_
| Array for the target profile for y.

## Detailed Description

Base class for distributed control problems with homogeneous Neumann boundary conditions, as formulated by Hans Mittelmann as Examples 4-6 in Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints.

Part 2: Distributed Control

Definition at line 50 of file MittelmannDistCntrlNeumA.hpp.

## Constructor & Destructor Documentation

MittelmannDistCntrlNeumABase::MittelmannDistCntrlNeumABase | ( |  | ) |

Constructor.

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

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

Default destructor.

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

## Member Function Documentation

virtual bool MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::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 MittelmannDistCntrlNeumABase::SetBaseParameters | ( | Index | N,
|  | Number | lb_y,
|  | Number | ub_y,
|  | Number | lb_u,
|  | Number | ub_u,
|  | Number | b_0j,
|  | Number | b_1j,
|  | Number | b_i0,
|  | Number | b_i1,
|  | 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 MittelmannDistCntrlNeumABase::y_d_cont | ( | Number | x1,
|  | Number | x2 |
| ) |  |  | const`[protected, pure virtual]`

Target profile function for y (and initial guess function).

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

Integrant in objective function.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont_dy | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

First partial derivative of fint_cont w.r.t.

y

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont_du | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

First partial derivative of fint_cont w.r.t.

u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont_dydy | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

Second partial derivative of fint_cont w.r.t.

y,y

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::fint_cont_dydy_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

y,y is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont_dudu | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

Second partial derivative of fint_cont w.r.t.

u,u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::fint_cont_dudu_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

u,u is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::fint_cont_dydu | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

Second partial derivative of fint_cont w.r.t.

y,u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::fint_cont_dydu_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

y,u is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

Forcing function for the elliptic equation.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont_dy | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

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

y

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont_du | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

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

u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont_dydy | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

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

y,y

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::d_cont_dydy_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

y,y is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont_dudu | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

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

u,u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::d_cont_dudu_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

y,y is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual Number MittelmannDistCntrlNeumABase::d_cont_dydu | ( | Number | x1,
|  | Number | x2,
|  | Number | y,
|  | Number | u |
| ) |  |  | const`[protected, pure virtual]`

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

y,u

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

virtual bool MittelmannDistCntrlNeumABase::d_cont_dydu_alwayszero | ( |  | ) | const`[protected, pure virtual]`

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

y,u is always zero.

Implemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

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

Overloaded Equals Operator.

Reimplemented from Ipopt::TNLP.

Reimplemented in MittelmannDistCntrlNeumA1, MittelmannDistCntrlNeumA2, and MittelmannDistCntrlNeumA3.

Index MittelmannDistCntrlNeumABase::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 234 of file MittelmannDistCntrlNeumA.hpp.

Index MittelmannDistCntrlNeumABase::u_index | ( | Index | i,
|  | Index | j |
| ) |  |  | const`[inline, private]`

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

Definition at line 240 of file MittelmannDistCntrlNeumA.hpp.

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

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

Definition at line 246 of file MittelmannDistCntrlNeumA.hpp.

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

Compute the grid coordinate for given index in x1 direction.

Definition at line 251 of file MittelmannDistCntrlNeumA.hpp.

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

Compute the grid coordinate for given index in x2 direction.

Definition at line 256 of file MittelmannDistCntrlNeumA.hpp.

## Member Data Documentation

Index MittelmannDistCntrlNeumABase::N_`[private]`

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

Definition at line 199 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::h_`[private]`

Step size.

Definition at line 201 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::hh_`[private]`

h_ squaredd

Definition at line 203 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::lb_y_`[private]`

overall lower bound on y

Definition at line 205 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::ub_y_`[private]`

overall upper bound on y

Definition at line 207 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::lb_u_`[private]`

overall lower bound on u

Definition at line 209 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::ub_u_`[private]`

overall upper bound on u

Definition at line 211 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_0j_`[private]`

Value of beta function (in Neumann boundary condition) for (0,x2) bounray.

Definition at line 214 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_1j_`[private]`

Value of beta function (in Neumann boundary condition) for (1,x2) bounray.

Definition at line 217 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_i0_`[private]`

Value of beta function (in Neumann boundary condition) for (x1,0) bounray.

Definition at line 220 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_i1_`[private]`

Value of beta function (in Neumann boundary condition) for (x1,1) bounray.

Definition at line 223 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::u_init_`[private]`

Initial value for the constrols u.

Definition at line 225 of file MittelmannDistCntrlNeumA.hpp.

Number* MittelmannDistCntrlNeumABase::y_d_`[private]`

Array for the target profile for y.

Definition at line 227 of file MittelmannDistCntrlNeumA.hpp.

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

- examples/ScalableProblems/MittelmannDistCntrlNeumA.hpp

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