[Ipopt] is this a bug? bad evaluation of the objective function at the optimum

[Pedro C. Alvarez]

Hi all,

I am starting to use Ipopt (through R interface), and I found this surprising 
'bug'(?) related to the value of the objective function at the optimum. Ipopt 
finds correctly the optimum, but the value of the objective at the optimum is 
incorrect.
I paste below the output of IPopt. Observe that at iteration #17 the value of 
the objective is worst that at #16 (which is approx the good value of the 
objective at the optimum). 

The problem I am trying to solve is a very easy convex problem with linear 
constraints.

Any clue would be appreciated?

thank very much,
Pedro.

------------------------------------------------------------------------------------------------
This is Ipopt version 3.12.0, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        8
Number of nonzeros in Lagrangian Hessian.............:        4

Total number of variables............................:        4
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        5
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        5
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  
ls
   0 -7.3757500e+01 0.00e+00 3.23e+01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   
0
   1 -8.9257486e+01 0.00e+00 3.20e+01  -1.0 1.70e+00    -  3.01e-02 1.10e-01f  
1
   2 -8.9941241e+01 0.00e+00 4.12e+01  -1.0 2.66e-01    -  9.10e-01 4.03e-02f  
1
   3 -8.9814517e+01 0.00e+00 1.42e-14  -1.0 3.57e-03    -  1.00e+00 1.00e+00f  
1
   4 -9.0308405e+01 0.00e+00 1.42e-14  -2.5 6.09e-03    -  1.00e+00 1.00e+00f  
1
   5 -9.0327373e+01 0.00e+00 1.42e-14  -3.8 2.34e-04    -  1.00e+00 1.00e+00f  
1
   6 -9.0328119e+01 0.00e+00 1.42e-14  -5.7 9.21e-06    -  1.00e+00 1.00e+00f  
1
   7 -9.0328122e+01 0.00e+00 2.11e+00  -8.6 1.13e-07    -  1.00e+00 3.95e-01f  
2
   8 -9.0328124e+01 0.00e+00 6.53e+00  -8.6 6.53e-08    -  1.00e+00 3.40e-01f  
2
   9 -9.0328125e+01 0.00e+00 1.60e+01  -8.6 3.70e-08    -  1.00e+00 3.00e-01f  
2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  
ls
  10 -9.0328125e+01 0.00e+00 3.75e+01  -8.6 1.74e-08    -  1.00e+00 3.99e-02f  
5
  11 -9.0328125e+01 0.00e+00 4.80e+01  -8.6 1.23e-08    -  1.00e+00 2.64e-02f  
6
  12 -9.0328125e+01 0.00e+00 5.15e+01  -8.6 1.06e-08    -  1.00e+00 7.46e-03f  
8
  13 -9.0328125e+01 0.00e+00 5.25e+01  -8.6 1.01e-08    -  1.00e+00 4.84e-04f 
12
  14 -9.0328125e+01 0.00e+00 5.27e+01  -8.6 1.00e-08    -  1.00e+00 2.44e-04f 
13
  15 -9.0328125e+01 0.00e+00 5.28e+01  -8.6 9.98e-09    -  1.00e+00 1.22e-04h 
14
  16 -9.0328125e+01 0.00e+00 5.28e+01  -8.6 9.97e-09    -  1.00e+00 6.10e-05h 
15
  17 -8.1203126e+01 0.00e+00 1.42e-14  -8.6 9.97e-09    -  1.00e+00 1.00e+00w  
1

Number of Iterations....: 17

                                   (scaled)                 (unscaled)
Objective...............:  -8.1203125989310649e+01   -8.1203125989310649e+01
Dual infeasibility......:   1.4210854715202004e-14    1.4210854715202004e-14
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   2.5161412838377742e-09    2.5161412838377742e-09
Overall NLP error.......:   2.5161412838377742e-09    2.5161412838377742e-09


Number of objective function evaluations             = 91
Number of objective gradient evaluations             = 18
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 91
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 18
Number of Lagrangian Hessian evaluations             = 17
Total CPU secs in IPOPT (w/o function evaluations)   =      0.009
Total CPU secs in NLP function evaluations           =      0.024

EXIT: Optimal Solution Found.






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        Pedro César Alvarez Esteban
        Dpto. de Estadística e Investigación Operativa
        Facultad de Ciencias
        Universidad de Valladolid
        Paseo de Belén, 7
        47011 Valladolid (SPAIN)
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        Tfo: +34 983 423930
        Fax: +34 983 423013
        E-mail: pedroc at eio.uva.es
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