Re: Fwd: Re: Infinite cycles

On 01/16/2017 11:59 PM, Andrew Makhorin wrote:
> 
>> the interesting thing about Matheu's example is that the infeasability
>> is constantly increasing over multiple orders of magnitude.
> 
> I'm unable to reproduce the effect. Glpsol with default options has no
> problem on solving Mathieu's example. If --norelax option is specified,
> the primal simplex falls into infinite loop, but this might be expected,
> because Harris' ratio test (that is, --relax option used by default)
> decreases the number of degenerate steps and thus prevents cycling in
> many cases. If the primal simplex fails, I'd recommend using --dual and
> --flip options.
> 
> 
> Andrew Makhorin
> 
> 

With GLPK 4.61 on Linux 64bit and --norelax it is not simply an infinite
loop. The infeasibility increases constantly as shown in the log below.

glpsol -m GLP_buggy_6d21.mod --norelax

*   500: obj =   1.262121212e+04 inf =   4.004e-15 (2)
*  1000: obj =   1.262121212e+04 inf =   1.052e-14 (2)
*  1500: obj =   1.262121212e+04 inf =   1.703e-14 (2)
*  2000: obj =   1.262121212e+04 inf =   2.355e-14 (2)
*  2500: obj =   1.262121212e+04 inf =   3.006e-14 (2)
*  3000: obj =   1.262121212e+04 inf =   3.658e-14 (2)
*  3500: obj =   1.262121212e+04 inf =   4.309e-14 (2)
*  4000: obj =   1.262121212e+04 inf =   4.961e-14 (2)
*  4500: obj =   1.262121212e+04 inf =   5.612e-14 (2)
*  5000: obj =   1.262121212e+04 inf =   6.264e-14 (2)
*  5500: obj =   1.262121212e+04 inf =   6.915e-14 (2)
*  6000: obj =   1.262121212e+04 inf =   7.567e-14 (2)
*  6500: obj =   1.262121212e+04 inf =   8.218e-14 (2)
*  7000: obj =   1.262121212e+04 inf =   8.870e-14 (2)
*  7500: obj =   1.262121212e+04 inf =   9.521e-14 (2)
*  8000: obj =   1.262121212e+04 inf =   1.017e-13 (2)
...
*177000: obj =   1.262121211e+04 inf =   2.304e-12 (2)
*177500: obj =   1.262121211e+04 inf =   2.310e-12 (2)
*178000: obj =   1.262121211e+04 inf =   2.317e-12 (2)
*178500: obj =   1.262121211e+04 inf =   2.323e-12 (2)
*179000: obj =   1.262121211e+04 inf =   2.330e-12 (2)
...
*826000: obj =   1.262121208e+04 inf =   1.076e-11 (2)
*826500: obj =   1.262121208e+04 inf =   1.077e-11 (2)
*827000: obj =   1.262121208e+04 inf =   1.077e-11 (2)
*827500: obj =   1.262121208e+04 inf =   1.078e-11 (2)
*828000: obj =   1.262121208e+04 inf =   1.079e-11 (2)
...
*10719000: obj =   1.262121156e+04 inf =   1.397e-10 (2)
*10719500: obj =   1.262121156e+04 inf =   1.397e-10 (2)
*10720000: obj =   1.262121156e+04 inf =   1.397e-10 (2)
*10720500: obj =   1.262121156e+04 inf =   1.397e-10 (2)
*10721000: obj =   1.262121156e+04 inf =   1.397e-10 (2)