[Help-glpk] infeasible optimal solution

[Chen Jiusheng]

Dear GLPK people,

          Thanks for GLPK, it is great work.

          GLPK 4.15 API routines were used in my application, the result is:

*******************Starting Optimization*******************

Objective: Max dr_glc6P

Status: solution is optimal.

Optimal objective value 0.031883 is found at: 

Reaction       NET         XCH         
Glucupt        1           0           
hxi            0.968       0           
pfk            0.8453      0           
eno            1.354       0           
pyk            0.4634      0           
gdh1           0.0001      0           
gdh2           0.0001      0           
rpe            -0.1117     0           
rpi            0.1118      0           
tk2            -0.08394    0           
tk1            -0.02779    0           
tal            -0.02779    0           
pdh1a          0.02293     0           
pdh1b          0.02293     0           
pdh2           -1.917e-015 0           
glta           -0.196      0           
icd1           0.1679      0           
icd2           0.1679      0           
akd1           0.0001      0           
akd2           0.0001      0           
akd3           0.0001      0           
fumA           0.0001      0           
fumB           0.0001      0           
fumC           0.364       0           
mdh            -0.7279     0           
gs1            -0.3639     0           
gs2            -0.3639     0           
ppc            -4.19       0           
pck            -5          0           
mez            0.0001      0           
dr_oaa1        0.2779      0           
dr_rib5p       0.1396      0           
dr_gap1        0.2527      0           
dr_gap3        0.2527      0           
dr_gap4        0.2527      0           
GAP_DPG        1.354       0           
AcCoA_Ac       1.104e-017  0           
Pyr_Lac        -1.593e-015 0           
dr_glc6P       0.03188     0           
dr_fru6P       0.01103     0           
dr_accoa       0.5829      0           
dr_pyr1        0.4406      0           
dr_akg         0.1678      0           
dr_akge        3.903e-015  0           
dr_oaa2        0.2779      0           
dr_oaa3        1.833e-015  0           
dr_rib5p2aux   0.1396      0           
dr_e4p         0.05615     0           
dr_pep         0.08073     0           
dr_gly         -2.002e-015 0           
dr_gap2        0           0           
dr_gap3_aux    0           0           
bs_co2         1.562e-016  0           
Lac_ex         -1.593e-015 0           
Ac_ex          1.104e-017  0           
Form_ex        -1.917e-015 0           
Eth_ex         -3.614e-016 0           

      0:   objval = -1.974571374e+000   infeas =  1.000000000e+000 (0)
     29:   objval =  2.830773108e-002   infeas =  0.000000000e+000 (0)
*    29:   objval =  2.830773108e-002   infeas =  0.000000000e+000 (0)
*    30:   objval =  3.188329160e-002   infeas =  1.332267630e-015 (0)
OPTIMAL SOLUTION FOUND




The result shows there exists optimal solution, consequently the optimal 
solution is assumed to be feasible.
However, there are small violations to the feasibility, such as that net value 
of Eth_ex (-3.614e-016), Form_ex (-1.917e-015), Lac_ex (-1.593e-015) and dr_gly 
(-2.002e-015), which should be >= 0.
Although they are extremely small discrepancies, it is not acceptable in my 
application, absolutely feasible must be guaranteed. 

Is there any method can be adopted to circumvent my problem? 
Any ideas will be greatly appreciated.

Many thanks,
J.S.Chen