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MittelmannDistCntrlNeumA.hpp
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1 // Copyright (C) 2005, 2006 International Business Machines and others.
2 // All Rights Reserved.
3 // This code is published under the Eclipse Public License.
4 //
5 // $Id: MittelmannDistCntrlNeumA.hpp 2005 2011-06-06 12:55:16Z stefan $
6 //
7 // Authors: Andreas Waechter IBM 2005-10-18
8 // based on MyNLP.hpp
9 
10 #ifndef __MITTELMANNDISTRCNTRLNEUMA_HPP__
11 #define __MITTELMANNDISTRCNTRLNEUMA_HPP__
12 
13 #include "IpTNLP.hpp"
14 #include "RegisteredTNLP.hpp"
15 
16 #ifdef HAVE_CONFIG_H
17 #include "config.h"
18 #else
19 #include "configall_system.h"
20 #endif
21 
22 #ifdef HAVE_CMATH
23 # include <cmath>
24 #else
25 # ifdef HAVE_MATH_H
26 # include <math.h>
27 # else
28 # error "don't have header file for math"
29 # endif
30 #endif
31 
32 #ifdef HAVE_CSTDIO
33 # include <cstdio>
34 #else
35 # ifdef HAVE_STDIO_H
36 # include <stdio.h>
37 # else
38 # error "don't have header file for stdio"
39 # endif
40 #endif
41 
42 using namespace Ipopt;
43 
51 {
52 public:
56 
59 
63  virtual bool get_nlp_info(Index& n, Index& m, Index& nnz_jac_g,
64  Index& nnz_h_lag, IndexStyleEnum& index_style);
65 
67  virtual bool get_bounds_info(Index n, Number* x_l, Number* x_u,
68  Index m, Number* g_l, Number* g_u);
69 
71  virtual bool get_starting_point(Index n, bool init_x, Number* x,
72  bool init_z, Number* z_L, Number* z_U,
73  Index m, bool init_lambda,
74  Number* lambda);
75 
77  virtual bool eval_f(Index n, const Number* x, bool new_x, Number& obj_value);
78 
80  virtual bool eval_grad_f(Index n, const Number* x, bool new_x, Number* grad_f);
81 
83  virtual bool eval_g(Index n, const Number* x, bool new_x, Index m, Number* g);
84 
89  virtual bool eval_jac_g(Index n, const Number* x, bool new_x,
90  Index m, Index nele_jac, Index* iRow, Index *jCol,
91  Number* values);
92 
97  virtual bool eval_h(Index n, const Number* x, bool new_x,
98  Number obj_factor, Index m, const Number* lambda,
99  bool new_lambda, Index nele_hess, Index* iRow,
100  Index* jCol, Number* values);
101 
103 
105  virtual bool get_scaling_parameters(Number& obj_scaling,
106  bool& use_x_scaling, Index n,
107  Number* x_scaling,
108  bool& use_g_scaling, Index m,
109  Number* g_scaling);
110 
115  virtual void finalize_solution(SolverReturn status,
116  Index n, const Number* x, const Number* z_L, const Number* z_U,
117  Index m, const Number* g, const Number* lambda,
118  Number obj_value,
119  const IpoptData* ip_data,
122 
123 protected:
127  void SetBaseParameters(Index N, Number lb_y,
128  Number ub_y, Number lb_u, Number ub_u,
129  Number b_0j, Number b_1j, Number b_i0, Number b_i1,
130  Number u_init);
131 
135  virtual Number y_d_cont(Number x1, Number x2) const =0;
137  virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const =0;
139  virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const =0;
141  virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const =0;
143  virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const =0;
146  virtual bool fint_cont_dydy_alwayszero() const =0;
148  virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const =0;
151  virtual bool fint_cont_dudu_alwayszero() const =0;
153  virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const =0;
156  virtual bool fint_cont_dydu_alwayszero() const =0;
158  virtual Number d_cont(Number x1, Number x2, Number y, Number u) const =0;
160  virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const =0;
162  virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const =0;
164  virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const =0;
167  virtual bool d_cont_dydy_alwayszero() const =0;
169  virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const =0;
172  virtual bool d_cont_dudu_alwayszero() const =0;
174  virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const =0;
177  virtual bool d_cont_dydu_alwayszero() const =0;
179 
180 private:
195 
229 
234  inline Index y_index(Index i, Index j) const
235  {
236  return j + (N_+2)*i;
237  }
240  inline Index u_index(Index i, Index j) const
241  {
242  return (N_+2)*(N_+2) + (j-1) + (N_)*(i-1);
243  }
246  inline Index pde_index(Index i, Index j) const
247  {
248  return (j-1) + N_*(i-1);
249  }
251  inline Number x1_grid(Index i) const
252  {
253  return h_*(Number)i;
254  }
256  inline Number x2_grid(Index i) const
257  {
258  return h_*(Number)i;
259  }
261 };
262 
265 {
266 public:
268  :
269  pi_(4.*atan(1.)),
270  alpha_(0.001)
271  {}
272 
274  {}
275 
276  virtual bool InitializeProblem(Index N)
277  {
278  if (N<1) {
279  printf("N has to be at least 1.");
280  return false;
281  }
282  Number lb_y = -1e20;
283  Number ub_y = 0.371;
284  Number lb_u = -8.;
285  Number ub_u = 9.;
286  Number b_0j = 1.;
287  Number b_1j = 1.;
288  Number b_i0 = 1.;
289  Number b_i1 = 1.;
290  Number u_init = (ub_u+lb_u)/2.;
291 
292  SetBaseParameters(N, lb_y, ub_y, lb_u, ub_u, b_0j, b_1j, b_i0, b_i1, u_init);
293  return true;
294  }
295 protected:
297  virtual Number y_d_cont(Number x1, Number x2) const
298  {
299  return sin(2.*pi_*x1)*sin(2.*pi_*x2);
300  }
302  virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
303  {
304  Number diff_y = y-y_d_cont(x1,x2);
305  return 0.5*(diff_y*diff_y + alpha_*u*u);
306  }
308  virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
309  {
310  return y-y_d_cont(x1,x2);
311  }
312 
314  virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
315  {
316  return alpha_*u;
317  }
319  virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
320  {
321  return 1.;
322  }
325  virtual bool fint_cont_dydy_alwayszero() const
326  {
327  return false;
328  }
330  virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
331  {
332  return alpha_;
333  }
336  virtual bool fint_cont_dudu_alwayszero() const
337  {
338  return false;
339  }
341  virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
342  {
343  return 0.;
344  }
347  virtual bool fint_cont_dydu_alwayszero() const
348  {
349  return true;
350  }
352  virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
353  {
354  return -exp(y) - u;
355  }
357  virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
358  {
359  return -exp(y);
360  }
362  virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
363  {
364  return -1.;
365  }
367  virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
368  {
369  return -exp(y);
370  }
373  virtual bool d_cont_dydy_alwayszero() const
374  {
375  return false;
376  }
378  virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
379  {
380  return 0.;
381  }
384  virtual bool d_cont_dudu_alwayszero() const
385  {
386  return true;
387  }
389  virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
390  {
391  return 0.;
392  }
395  virtual bool d_cont_dydu_alwayszero() const
396  {
397  return true;
398  }
399 private:
405 
406  const Number pi_;
408  const Number alpha_;
409 };
410 
413 {
414 public:
416  :
417  pi_(4.*atan(1.))
418  {}
419 
421  {}
422 
423  virtual bool InitializeProblem(Index N)
424  {
425  if (N<1) {
426  printf("N has to be at least 1.");
427  return false;
428  }
429  Number lb_y = -1e20;
430  Number ub_y = 0.371;
431  Number lb_u = -8.;
432  Number ub_u = 9.;
433  Number b_0j = 1.;
434  Number b_1j = 1.;
435  Number b_i0 = 1.;
436  Number b_i1 = 1.;
437  Number u_init = (ub_u+lb_u)/2.;
438 
439  SetBaseParameters(N, lb_y, ub_y, lb_u, ub_u, b_0j, b_1j, b_i0, b_i1, u_init);
440  return true;
441  }
442 protected:
444  virtual Number y_d_cont(Number x1, Number x2) const
445  {
446  return sin(2.*pi_*x1)*sin(2.*pi_*x2);
447  }
449  virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
450  {
451  Number diff_y = y-y_d_cont(x1,x2);
452  return 0.5*diff_y*diff_y;
453  }
455  virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
456  {
457  return y-y_d_cont(x1,x2);
458  }
459 
461  virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
462  {
463  return 0.;
464  }
466  virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
467  {
468  return 1.;
469  }
472  virtual bool fint_cont_dydy_alwayszero() const
473  {
474  return false;
475  }
477  virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
478  {
479  return 0.;
480  }
483  virtual bool fint_cont_dudu_alwayszero() const
484  {
485  return true;
486  }
488  virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
489  {
490  return 0.;
491  }
494  virtual bool fint_cont_dydu_alwayszero() const
495  {
496  return true;
497  }
499  virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
500  {
501  return -exp(y) - u;
502  }
504  virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
505  {
506  return -exp(y);
507  }
509  virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
510  {
511  return -1.;
512  }
514  virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
515  {
516  return -exp(y);
517  }
520  virtual bool d_cont_dydy_alwayszero() const
521  {
522  return false;
523  }
525  virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
526  {
527  return 0.;
528  }
531  virtual bool d_cont_dudu_alwayszero() const
532  {
533  return true;
534  }
536  virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
537  {
538  return 0.;
539  }
542  virtual bool d_cont_dydu_alwayszero() const
543  {
544  return true;
545  }
546 private:
552 
553  const Number pi_;
554 };
555 
558 {
559 public:
561  :
562  pi_(4.*atan(1.)),
563  M_(1.),
564  K_(0.8),
565  b_(1.)
566  {}
567 
569  {}
570 
571  virtual bool InitializeProblem(Index N)
572  {
573  if (N<1) {
574  printf("N has to be at least 1.");
575  return false;
576  }
577  Number lb_y = 3.;//-1e20;
578  Number ub_y = 6.09;
579  Number lb_u = 1.4;
580  Number ub_u = 1.6;
581  Number b_0j = 1.;
582  Number b_1j = 0.;
583  Number b_i0 = 1.;
584  Number b_i1 = 0.;
585  Number u_init = (ub_u+lb_u)/2.;
586 
587  SetBaseParameters(N, lb_y, ub_y, lb_u, ub_u, b_0j, b_1j, b_i0, b_i1, u_init);
588  return true;
589  }
590 protected:
592  virtual Number y_d_cont(Number x1, Number x2) const
593  {
594  return 6.;
595  }
597  virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
598  {
599  return u*(M_*u - K_*y);
600  }
602  virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
603  {
604  return -K_*u;
605  }
606 
608  virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
609  {
610  return 2.*M_*u - K_*y;
611  }
613  virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
614  {
615  return 0.;
616  }
619  virtual bool fint_cont_dydy_alwayszero() const
620  {
621  return true;
622  }
624  virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
625  {
626  return 2.*M_;
627  }
630  virtual bool fint_cont_dudu_alwayszero() const
631  {
632  return false;
633  }
635  virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
636  {
637  return -K_;
638  }
641  virtual bool fint_cont_dydu_alwayszero() const
642  {
643  return false;
644  }
646  virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
647  {
648  return y*(u + b_*y - a(x1,x2));
649  }
651  virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
652  {
653  return (u + 2.*b_*y -a(x1,x2));
654  }
656  virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
657  {
658  return y;
659  }
661  virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
662  {
663  return 2.*b_;
664  }
667  virtual bool d_cont_dydy_alwayszero() const
668  {
669  return false;
670  }
672  virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
673  {
674  return 0.;
675  }
678  virtual bool d_cont_dudu_alwayszero() const
679  {
680  return true;
681  }
683  virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
684  {
685  return 1.;
686  }
689  virtual bool d_cont_dydu_alwayszero() const
690  {
691  return false;
692  }
693 private:
699 
700  const Number pi_;
701  /*@name constrants appearing in problem formulation */
703  const Number M_;
704  const Number K_;
705  const Number b_;
707  //* Auxiliary function for state equation */
708  inline Number a(Number x1, Number x2) const
709  {
710  return 7. + 4.*sin(2.*pi_*x1*x2);
711  }
712 };
713 
714 #endif
virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
Integrant in objective function.
Index u_index(Index i, Index j) const
Translation of mesh point indices to NLP variable indices for u(x_ij)
Number * x
Input: Starting point Output: Optimal solution.
virtual bool d_cont_dydu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
virtual Number y_d_cont(Number x1, Number x2) const
Target profile function for y.
const Number pi_
Value of pi (made available for convenience)
virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
Forcing function for the elliptic equation.
virtual bool fint_cont_dydu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
Class for all IPOPT specific calculated quantities.
virtual bool fint_cont_dudu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
Number * y_d_
Array for the target profile for y.
Number Number Index Number Number Index Index Index index_style
indexing style for iRow &amp; jCol, 0 for C style, 1 for Fortran style
Number x2_grid(Index i) const
Compute the grid coordinate for given index in x2 direction.
Class implementating Example 6.
Number Number Index m
Number of constraints.
const Number pi_
Value of pi (made available for convenience)
virtual bool d_cont_dydu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
Number Number * g
Values of constraint at final point (output only - ignored if set to NULL)
virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t y,y.
Number Number Index Number Number Index Index Index Eval_F_CB Eval_G_CB Eval_Grad_F_CB Eval_Jac_G_CB Eval_H_CB eval_h
Callback function for evaluating Hessian of Lagrangian function.
Number ub_u_
overall upper bound on u
virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
double Number
Type of all numbers.
Definition: IpTypes.hpp:17
virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
virtual bool d_cont_dydu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
Number lb_u_
overall lower bound on u
virtual bool d_cont_dudu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t y,y.
Index pde_index(Index i, Index j) const
Translation of interior mesh point indices to the corresponding PDE constraint number.
Number Number Index Number Number Index Index Index Eval_F_CB Eval_G_CB Eval_Grad_F_CB eval_grad_f
Callback function for evaluating gradient of objective function.
virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
Integrant in objective function.
virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
Class implementating Example 5.
virtual Number y_d_cont(Number x1, Number x2) const
Profile function for initial y.
const Number pi_
Value of pi (made available for convenience)
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.
virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
Number Number Index Number Number Index Index Index Eval_F_CB Eval_G_CB Eval_Grad_F_CB Eval_Jac_G_CB eval_jac_g
Callback function for evaluating Jacobian of constraint functions.
virtual bool fint_cont_dydu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
Number u_init_
Initial value for the constrols u.
SolverReturn
enum for the return from the optimize algorithm (obviously we need to add more)
Definition: IpAlgTypes.hpp:22
virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
Number Number Index Number Number Index nele_jac
Number of non-zero elements in constraint Jacobian.
virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual bool InitializeProblem(Index N)
Initialize internal parameters, where N is a parameter determining the problme size.
virtual Number fint_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
virtual bool InitializeProblem(Index N)
Initialize internal parameters, where N is a parameter determining the problme size.
Class implementating Example 4.
virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual bool fint_cont_dydy_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
Class to organize all the data required by the algorithm.
Definition: IpIpoptData.hpp:83
Number Number Index Number Number Index Index Index Eval_F_CB Eval_G_CB eval_g
Callback function for evaluating constraint functions.
Index y_index(Index i, Index j) const
Translation of mesh point indices to NLP variable indices for y(x_ij)
virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
int Index
Type of all indices of vectors, matrices etc.
Definition: IpTypes.hpp:19
Number b_i0_
Value of beta function (in Neumann boundary condition) for (x1,0) bounray.
Number ub_y_
overall upper bound on y
virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
Number b_1j_
Value of beta function (in Neumann boundary condition) for (1,x2) bounray.
virtual Number d_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
virtual bool d_cont_dudu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
Number Number * x_scaling
virtual Number fint_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual bool fint_cont_dydu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
virtual bool fint_cont_dydy_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
const Number alpha_
Value for parameter alpha in objective functin.
Number Number Index Number Number Index Index nele_hess
Number of non-zero elements in Hessian of Lagrangian.
Number a(Number x1, Number x2) const
virtual Number d_cont_dydy(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t y,y.
Class implemented the NLP discretization of.
virtual bool d_cont_dydy_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
Number Number Number * g_scaling
Index N_
Number of mesh points in one dimension (excluding boundary)
virtual bool d_cont_dydy_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
virtual Number fint_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
IndexStyleEnum
overload this method to return the number of variables and constraints, and the number of non-zeros i...
Definition: IpTNLP.hpp:80
virtual bool fint_cont_dudu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
virtual bool InitializeProblem(Index N)
Initialize internal parameters, where N is a parameter determining the problme size.
virtual bool fint_cont_dydy_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
Number lb_y_
overall lower bound on y
Number b_i1_
Value of beta function (in Neumann boundary condition) for (x1,1) bounray.
virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
Forcing function for the elliptic equation.
virtual Number d_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
virtual bool d_cont_dydy_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.
virtual Number d_cont_du(Number x1, Number x2, Number y, Number u) const
First partial derivative of forcing function w.r.t.
virtual Number y_d_cont(Number x1, Number x2) const
Target profile function for y.
virtual bool fint_cont_dudu_alwayszero() const
returns true if second partial derivative of fint_cont w.r.t.
virtual Number fint_cont_dy(Number x1, Number x2, Number y, Number u) const
First partial derivative of fint_cont w.r.t.
Number obj_scaling
virtual Number d_cont_dydu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of forcing function w.r.t.
Number Number Index Number Number Index Index Index Eval_F_CB eval_f
Callback function for evaluating objective function.
virtual Number fint_cont_dudu(Number x1, Number x2, Number y, Number u) const
Second partial derivative of fint_cont w.r.t.
virtual Number fint_cont(Number x1, Number x2, Number y, Number u) const
Integrant in objective function.
Number x1_grid(Index i) const
Compute the grid coordinate for given index in x1 direction.
Number b_0j_
Value of beta function (in Neumann boundary condition) for (0,x2) bounray.
virtual Number d_cont(Number x1, Number x2, Number y, Number u) const
Forcing function for the elliptic equation.
virtual bool d_cont_dudu_alwayszero() const
returns true if second partial derivative of d_cont w.r.t.