Cycling in Ipopt

[matheusdiogenesandrade]

Hello folks!

This question was also place in another forum (https://or.stackexchange.com/questions/11666/cycling-in-ipopt).

I am running a QCQP model in the following setup

• AMPL;
• MUMPS 5.6.2; And
• Ipopt 3.14.14, with the following parameters (cf. https://coin-or.github.io/Ipopt/OPTIONS.html):
  • check_derivatives_for_naninf=yes;
  • hessian_approximation=limited-memory;
  • hessian_approximation_space=nonlinear-variables;
  • inf_pr_output=internal;
  • line_search_method=cg-penalty;
  • max_iter=10000000;
  • mu_strategy=adaptive.

With the following Ipopt header.

Number of nonzeros in equality constraint Jacobian...:     3072
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        0
Total number of variables............................:     1024
                     variables with only lower bounds:        0
                variables with lower and upper bounds:     1024
                     variables with only upper bounds:        0
Total number of equality constraints.................:       65
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

And the following iteration log.

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
33480  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33481  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33482  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33483  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33484  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33485  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33486  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33487  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33488  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33489  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
33490  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33491  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33492  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33493  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33494  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33495  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33496  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33497  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33498  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33499  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
33500  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33501  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33502  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33503  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33504  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33505  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33506  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
33507  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
33508  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
33509  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
(REPEATS) 33510  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33511  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33512  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33513  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33514  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33515  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33516  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33517  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33518  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33519  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
(REPEATS) 33520  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33521  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33522  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33523  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33524  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33525  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33526  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33527  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33528  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33529  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
(REPEATS) 33530  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33531  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33532  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33533  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33534  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33535  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33536  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2
(REPEATS) 33537  3.1818420e-01 9.96e-01 3.36e-02  -1.2 3.24e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33538  3.1812523e-01 9.96e-01 3.12e-02  -1.2 3.00e-07    -  1.00e+00 1.00e+00c  1
(REPEATS) 33539  3.1799341e-01 9.96e-01 5.23e+04  -1.2 1.21e-06    -  1.00e+00 4.96e-01c  2

Note that, the first 30 log entries keep repeating. In my execution, this behaviour keeps up for hours. Unfortunately, I am too naive in the realms of Interior Point Methods (IPM), thus I am not that keen in what regards conjecturing the possible reason for this. I would like to know if someone has any suggestion of what may be the reason.

By the way, the inputted problem is feasible.

Thanks and regards.

[svigerske]

I could imagine that this is caused by changing the line search method from filter to cg-penalty. Probably a filter method is better in avoiding cycling, since it looks at objective value and infeasibility separately.

The docu says Only the "filter" choice is officially supported. I suppose cg-penalty is not much tested.

[matheusdiogenesandrade]

I could imagine that this is caused by changing the line search method from filter to cg-penalty. Probably a filter method is better in avoiding cycling, since it looks at objective value and infeasibility separately.

The docu says Only the "filter" choice is officially supported. I suppose cg-penalty is not much tested.

Thanks for the answer. Actually, the filter option, for my case, led to infeasibilities. But thanks for the comment. I wil maked this issue as closed, till I get a better understanding of the root cause. Regards.