NAG Library Manual, Mark 30
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NAG CPP Interface Introduction
Example description

nagcpp::opt::handle_solve_lp_ipm Example
                                                                                
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  E04MT, Interior point method for LP problems                                  
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 Begin of Options                                                               
     Print File                    =                   6     * d                
     Print Level                   =                   2     * d                
     Print Options                 =                 Yes     * d                
     Print Solution                =                 All     * U                
     Monitoring File               =                  -1     * d                
     Monitoring Level              =                   4     * d                
     Lpipm Monitor Frequency       =                   1     * U                
 
     Infinite Bound Size           =         1.00000E+20     * d                
     Task                          =            Minimize     * d                
     Stats Time                    =                  No     * d                
 
     Lp Presolve                   =                 Yes     * d                
     Lpipm Algorithm               =         Primal-dual     * d                
     Lpipm Centrality Correctors   =                  -6     * U                
     Lpipm Iteration Limit         =                 100     * d                
     Lpipm Max Iterative Refinement=                   5     * d                
     Lpipm Scaling                 =          Arithmetic     * d                
     Lpipm Stop Tolerance          =         1.00000E-10     * U                
     Lpipm Stop Tolerance 2        =         2.67452E-10     * d                
     Lpipm System Formulation      =                Auto     * d                
 End of Options                                                                 
                                                                                
 Problem Statistics                                                                                                                                                                                     
   No of variables                  7                                                                                                                                                                   
     free (unconstrained)           0                                                                                                                                                                   
     bounded                        7                                                                                                                                                                   
   No of lin. constraints           7                                                                                                                                                                   
     nonzeroes                     41                                                                                                                                                                   
   Objective function          Linear                                                                                                                                                                   
                                                                                                                                                                                                        
 Presolved Problem Measures                                                     
   No of variables                 13                                           
     free (unconstrained)           0                                           
   No of lin. constraints           7                                           
     nonzeroes                     47                                           
                                                                                
                                                                                
 ------------------------------------------------------------------------------ 
  it|    pobj    |    dobj    |  optim  |  feas   |  compl  |   mu   | mcc | I  
 ------------------------------------------------------------------------------ 
   0 -7.86591E-02  1.71637E-02  1.27E+00  1.06E+00  8.89E-02  1.5E-01           
   1  5.74135E-03 -2.24369E-02  6.11E-16  1.75E-01  2.25E-02  2.8E-02   0       
   2  1.96803E-02  1.37067E-02  5.06E-16  2.28E-02  2.91E-03  3.4E-03   0       
   3  2.15232E-02  1.96162E-02  7.00E-15  9.24E-03  1.44E-03  1.7E-03   0       
   4  2.30321E-02  2.28676E-02  1.15E-15  2.21E-03  2.97E-04  3.4E-04   0       
   5  2.35658E-02  2.35803E-02  1.32E-15  1.02E-04  8.41E-06  9.6E-06   0       
   6  2.35965E-02  2.35965E-02  1.64E-15  7.02E-08  6.35E-09  7.2E-09   0       
Iteration 7
monit() reports good approximate solution (tol = 1.2e-08):
   7  2.35965E-02  2.35965E-02  1.35E-15  3.52E-11  3.18E-12  3.6E-12   0       
 ------------------------------------------------------------------------------ 
 Status: converged, an optimal solution found                                   
 ------------------------------------------------------------------------------ 
 Final primal objective value         2.359648E-02                              
 Final dual objective value           2.359648E-02                              
 Absolute primal infeasibility        4.168797E-15                              
 Relative primal infeasibility        3.518607E-11                              
 Absolute dual infeasibility          5.084353E-11                              
 Relative dual infeasibility          1.350467E-15                              
 Absolute complementarity gap         2.685778E-11                              
 Relative complementarity gap         3.175366E-12                              
 Iterations                                      7                              
                                                                                
 Primal variables:                                                              
   idx   Lower bound       Value       Upper bound                              
     1  -1.00000E-02   -1.00000E-02    1.00000E-02                              
     2  -1.00000E-01   -1.00000E-01    1.50000E-01                              
     3  -1.00000E-02    3.00000E-02    3.00000E-02                              
     4  -4.00000E-02    2.00000E-02    2.00000E-02                              
     5  -1.00000E-01   -6.74853E-02    5.00000E-02                              
     6  -1.00000E-02   -2.28013E-03         inf                                 
     7  -1.00000E-02   -2.34528E-04         inf                                 
                                                                                
 Box bounds dual variables:                                                     
   idx   Lower bound       Value       Upper bound       Value                  
     1  -1.00000E-02    3.30098E-01    1.00000E-02    0.00000E+00               
     2  -1.00000E-01    1.43844E-02    1.50000E-01    0.00000E+00               
     3  -1.00000E-02    0.00000E+00    3.00000E-02    9.09967E-02               
     4  -4.00000E-02    0.00000E+00    2.00000E-02    7.66124E-02               
     5  -1.00000E-01    3.51391E-11    5.00000E-02    0.00000E+00               
     6  -1.00000E-02    3.42902E-11         inf       0.00000E+00               
     7  -1.00000E-02    8.61040E-12         inf       0.00000E+00               
                                                                                
 Linear constraints dual variables:                                             
   idx   Lower bound       Value       Upper bound       Value                  
     1  -1.30000E-01    0.00000E+00   -1.30000E-01    1.43111E+00               
     2       -inf       0.00000E+00   -4.90000E-03    4.00339E-10               
     3       -inf       0.00000E+00   -6.40000E-03    1.54305E-08               
     4       -inf       0.00000E+00   -3.70000E-03    3.80136E-10               
     5       -inf       0.00000E+00   -1.20000E-03    4.72629E-11               
     6  -9.92000E-02    1.50098E+00         inf       0.00000E+00               
     7  -3.00000E-03    1.51661E+00    2.00000E-03    0.00000E+00