Re: [Help-glpk] Assertion failed

[Andrew Makhorin]

I slightly modified lp relaxation of your problem to avoid the error
in glpk simplex solver as follows:

------------------------------------------------------------------------
Minimize
 obj: x_1

Subject To
 r_1: - 1003 x_1 + x_2 >= 0
 r_2: - 1999 x_2 + x_3 >= 0
 r_3: - 4000 x_3 + x_4 >= 0
 r_4: + 8000 x_4 + x_5 <= 0
 r_5: + 2 x_5 + x_6 >= 0
\ r_6: - x_1 <= -1002
\ r_7: - x_2 <= -1005006
\ r_8: - x_3 <= 138476654
\ r_9: - x_4 <= -144165184
\ r_10: - x_6 <= -1

Bounds
 x_1 >= 1002
 x_2 >= 1005006
 x_3 >= -138476654
 x_4 >= 144165184
 x_5 free
 x_6 >= 1
------------------------------------------------------------------------

And using options --nopresol --std --noscale I managed to obtain the
optimal solution of lp relaxation:

------------------------------------------------------------------------
Problem:
Rows:       5
Columns:    6
Non-zeros:  10
Status:     OPTIMAL
Objective:  obj = 1002 (MINimum)

   No.   Row name   St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 r_1          B              0             0               
     2 r_2          NL             0             0                       < eps
     3 r_3          NL             0             0                       < eps
     4 r_4          NU             0                           0         < eps
     5 r_5          NL             0             0                       < eps

   No. Column name  St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 x_1          NL          1002          1002                           1
     2 x_2          NL   1.00501e+06   1.00501e+06                       < eps
     3 x_3          B    2.00901e+09  -1.38477e+08               
     4 x_4          B    8.03603e+12   1.44165e+08               
     5 x_5          B   -6.42882e+16                             
     6 x_6          B    1.28576e+17             1               

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err. = 0.00e+00 on row 0
        max.rel.err. = 0.00e+00 on row 0
        High quality

KKT.PB: max.abs.err. = 0.00e+00 on row 0
        max.rel.err. = 0.00e+00 on row 0
        High quality

KKT.DE: max.abs.err. = 0.00e+00 on column 0
        max.rel.err. = 0.00e+00 on column 0
        High quality

KKT.DB: max.abs.err. = 0.00e+00 on row 0
        max.rel.err. = 0.00e+00 on row 0
        High quality

End of output
------------------------------------------------------------------------

You may note that x_3 x_4 x_5 and x_6 have too large values and cannot
be modelled as integer variables.

(Btw, within a tolerance 1e-6 the solution is integer feasible :)


Andrew Makhorin