[Ipopt] ipopt with l-bfgs: slow progress on unbounded linear objective

Sat Jun 20 07:36:14 EDT 2015

Interesting. I have modified and attached Ipopt/examples/Cpp_example/ to
demonstrate the issue.

Not sure why, but app->Options()->SetNumericValue("print_level", 8); does
not generate extra output, so I cannot directly compare our log files. THe
output below is for Ipopt 3.12.3, but I was able to reproduce this issue
with Ipopt 3.11.

~/IPOPT/build/Ipopt/examples/Cpp_example$ ./cpp_example | head -n 100

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear
optimization.
 Ipopt is released as open source code under the Eclipse Public License
(EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

This is Ipopt version 3.12.3, running with linear solver ma27.

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

Total number of variables............................:        1
                     variables with only lower bounds:        1
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
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

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
   0 -1.0000000e+00 0.00e+00 2.00e+00   0.0 0.00e+00    -  0.00e+00
0.00e+00   0
   1 -1.0933387e+01 0.00e+00 1.01e+00   1.0 9.93e+00    -  9.84e-01
1.00e+00f  1
   2 -2.0934581e+01 0.00e+00 1.00e+00  -1.0 1.00e+01    -  1.00e+00
1.00e+00f  1
   3 -3.0934593e+01 0.00e+00 1.00e+00  -2.9 1.00e+01    -  1.00e+00
1.00e+00f  1
   4 -4.0934594e+01 0.00e+00 1.00e+00  -4.9 1.00e+01    -  1.00e+00
1.00e+00f  1

On Sat, Jun 20, 2015 at 6:53 AM, Stefan Vigerske <stefan at math.hu-berlin.de>
wrote:

> Hi,
>
> I cannot reproduce this behavior (and I assume you mean that x is
> increasing only slowly, not decreasing).
> Even when putting x>=0 as a constraint instead of just a variable bound,
> Ipopt reports unboundedness after 35 iterations.
>
> The values for x in all iterations are
> curr_x[    1]{x}= 0.0000000000000000e+00
> curr_x[    1]{x}= 1.0000000000000000e+04
> curr_x[    1]{x}= 4.0000000000000000e+04
> curr_x[    1]{x}= 1.3000000000000000e+05
> curr_x[    1]{x}= 4.0000000000000000e+05
> curr_x[    1]{x}= 1.2100000000000000e+06
> curr_x[    1]{x}= 3.6400000000000005e+06
> curr_x[    1]{x}= 1.0930000000000002e+07
> curr_x[    1]{x}= 3.2800000000000007e+07
> curr_x[    1]{x}= 9.8410000000000030e+07
> curr_x[    1]{x}= 2.9524000000000012e+08
> curr_x[    1]{x}= 8.8573000000000036e+08
> curr_x[    1]{x}= 2.6572000000000010e+09
> curr_x[    1]{x}= 7.9716100000000029e+09
> curr_x[    1]{x}= 2.3914840000000011e+10
> curr_x[    1]{x}= 7.1744530000000046e+10
> curr_x[    1]{x}= 2.1523360000000012e+11
> curr_x[    1]{x}= 6.4570081000000037e+11
> curr_x[    1]{x}= 1.9371024400000010e+12
> curr_x[    1]{x}= 5.8113073300000039e+12
> curr_x[    1]{x}= 1.7433922000000012e+13
> curr_x[    1]{x}= 5.2301766010000031e+13
> curr_x[    1]{x}= 1.5690529804000012e+14
> curr_x[    1]{x}= 4.7071589413000044e+14
> curr_x[    1]{x}= 1.4121476824000012e+15
> curr_x[    1]{x}= 4.2364430472100040e+15
> curr_x[    1]{x}= 1.2709329141640014e+16
> curr_x[    1]{x}= 3.8127987424930048e+16
> curr_x[    1]{x}= 1.1438396227480014e+17
> curr_x[    1]{x}= 3.4315188682441050e+17
> curr_x[    1]{x}= 1.0294556604732416e+18
> curr_x[    1]{x}= 3.0883669814197350e+18
> curr_x[    1]{x}= 9.2651009442592154e+18
> curr_x[    1]{x}= 2.7795302832777658e+19
> curr_x[    1]{x}= 8.3385908498332975e+19
> curr_x[    1]{x}= 1.8338590849833298e+20
>
> I attach the full log.
>
> If I define x>=0 as variable bound, then Ipopt needs only 6 iterations.
>
> Stefan
>
>
>
> On 06/18/2015 05:49 PM, Ipopt User wrote:
>
>> When I try to solve the simple scalar problem min{-x : x >= 0} with IPOPT
>> and use hessian_approximation = limited-memory, the progress is very slow.
>> Essentially, x is reduced by 1 in each iteration.
>>
>>  From what I understand, this is due to the Hessian approximation, which
>> in
>> this case is just the identity matrix (plus 1/x due to the log barrier
>> term, which is significant only in the first few iterations). Solving Hs =
>> -g, with H the Hessian, s the step and g the gradient, it finds s = 1.
>> Indeed when I set limited_memory_init_val = 0.1, x is reduced by 10 in
>> each
>> iteration.
>>
>> This seems undesirable to me. Other L-BFGS based solvers like SNOPT and
>> L-BFGS-B figure out that the problem is unbounded in a few iterations.
>>
>>
>>
>> _______________________________________________
>> Ipopt mailing list
>> Ipopt at list.coin-or.org
>> http://list.coin-or.org/mailman/listinfo/ipopt
>>
>>
>
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