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>

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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 34 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 218 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 224 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 230 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 235 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 240 of file MittelmannDistCntrlNeumA.hpp.

Member Data Documentation

Index MittelmannDistCntrlNeumABase::N_ [private]

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

Definition at line 183 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::h_ [private]

Step size.

Definition at line 185 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::hh_ [private]

h_ squaredd

Definition at line 187 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::lb_y_ [private]

overall lower bound on y

Definition at line 189 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::ub_y_ [private]

overall upper bound on y

Definition at line 191 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::lb_u_ [private]

overall lower bound on u

Definition at line 193 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::ub_u_ [private]

overall upper bound on u

Definition at line 195 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_0j_ [private]

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

Definition at line 198 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_1j_ [private]

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

Definition at line 201 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_i0_ [private]

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

Definition at line 204 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::b_i1_ [private]

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

Definition at line 207 of file MittelmannDistCntrlNeumA.hpp.

Number MittelmannDistCntrlNeumABase::u_init_ [private]

Initial value for the constrols u.

Definition at line 209 of file MittelmannDistCntrlNeumA.hpp.

Number* MittelmannDistCntrlNeumABase::y_d_ [private]

Array for the target profile for y.

Definition at line 211 of file MittelmannDistCntrlNeumA.hpp.

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