[Help-glpk] Problem infeasible is feasible for glpsol

[Nicolo Giorgetti]

Dear All,

Find below a very simple problem (outpb.lp) which is infeasible by
construction (row r_1 defines x_1 >=0 whereas r_6 x_1<=-1e-006).
Although there is no feasible solution for x_1 glpsol gives the
following output:

$ glpsol --cpxlp outpb.lp  -o sol
lpx_read_cpxlp: reading problem data from `outpb.lp'...
lpx_read_cpxlp: 8 rows, 2 columns, 8 non-zeros
lpx_read_cpxlp: 20 lines were read
lpx_simplex: original LP has 8 rows, 2 columns, 8 non-zeros
Objective value = 0
OPTIMAL SOLUTION FOUND BY LP PRESOLVER
Time used:   0.0 secs
Memory used: 0.1M (66340 bytes)

Solution is attached below.

I don't understand why glpsol returns a feasible solution. Could
anybody give me an explanation? Thanks!

Regards,
Nicolo Giorgetti.


-------------- outpb.lp ----------------------------------------

\* Problem: Unknown *\

Minimize
 obj: 0 x_1

Subject To
 r_1: - x_1 <= 0
 r_2: + 0.1 x_1 <= 1.000001
 r_3: + 0.0633975908526212 x_2 <= 1.000001
 r_4: - 0.0633975908526212 x_2 <= 1.000001
 r_5: - 0.1 x_1 <= 1.000001
 r_6: + x_1 <= -1e-006
 r_7: - 0.0633975908526212 x_2 <= 1.000001
 r_8: + 0.0633975908526212 x_2 <= 1.000001

Bounds
 -10 <= x_1 <= 10
 -10 <= x_2 <= 10

End

-------------- outpb.lp ----------------------------------------



-------------- sol ---------------------------------------------

Problem:
Rows:       8
Columns:    2
Non-zeros:  8
Status:     OPTIMAL
Objective:  obj = 0 (MINimum)

   No.   Row name   St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 r_1          NU             0                           0         < eps
     2 r_2          B              0                           1 
     3 r_3          B      -0.633976                           1 
     4 r_4          B       0.633976                           1 
     5 r_5          B              0                           1 
     6 r_6          B              0                     -1e-006 
     7 r_7          B       0.633976                           1 
     8 r_8          B      -0.633976                           1 

   No. Column name  St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 x_1          B              0           -10            10 
     2 x_2          NL           -10           -10            10         < eps

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err. = 0.00e+000 on row 0
        max.rel.err. = 0.00e+000 on row 0
        High quality

KKT.PB: max.abs.err. = 1.00e-006 on row 6
        max.rel.err. = 1.00e-006 on row 6
        Medium quality

KKT.DE: max.abs.err. = 0.00e+000 on column 0
        max.rel.err. = 0.00e+000 on column 0
        High quality

KKT.DB: max.abs.err. = 0.00e+000 on row 0
        max.rel.err. = 0.00e+000 on row 0
        High quality

End of output

-------------- sol ---------------------------------------------