# Infeasibility in LP when solving MILP

Question asked by sean.ma@energyexemplar.com on Aug 11, 2015

Hi,

When solving an MILP problem using Xpress, the LP problems are infeasible after LP relaxation was tightened. However, the optimal solution is obtained at the end. Also, what's the names of infeasible LP problems, for example -MAAA and -NAAA?

Here is the logging messages from Xpress:

Minimizing MILP \

Original problem has:

848005 rows       563160 cols      2825874 elements     17448 globals

Presolved problem has:

232410 rows       233233 cols      1124476 elements     16488 globals

LP relaxation tightened

Symmetric problem: generators: 423, support set: 15553

Number of orbits: 4526, largest orbit: 20

Minimizing LP \-MAAA

Original problem has:

232410 rows       233233 cols      1124476 elements

The problem is infeasible due to row R43832

Minimizing LP \-NAAA

Original problem has:

232410 rows       233233 cols      1124476 elements

The problem is infeasible due to row R43832

Barrier cache sizes : L1=32K L2=25600K

Using AVX support

Cores per CPU (CORESPERCPU): 16

Crossover starts

Its         Obj Value      S   Ninf  Nneg        Sum Inf  Time

10061       30077657.97      P      0     0        .000000    41

25338       30077657.97      N      0     0        .000000    41

26706       30077657.97      D      0     5        .000000    55

0       30077657.97      P      0     4        .000000    55

4       30077657.97      P      0     0        .000000    55

Optimal solution found

Starting root cutting & heuristics

Its Type    BestSoln    BestBound   Sols    Add    Del     Gap     GInf   Time

+         30152432.34  30077657.97      1                  0.25%       0     93

*** MIP gap is less than MIPABSSTOP/MIPRELSTOP ***

*** Search completed ***     Time:    93 Nodes:          0

Number of integer feasible solutions found is 1

Best integer solution found is  30152432.34

Best bound is  30077657.97

Uncrunching matrix

Minimizing LP \

Original problem has:

848005 rows       563160 cols      2825874 elements

Presolved problem has:

62394 rows       112601 cols       663349 elements

Barrier cache sizes : L1=32K L2=25600K

Using AVX support

Cores per CPU (CORESPERCPU): 16

Crossover starts

Its         Obj Value      S   Ninf  Nneg        Sum Inf  Time

10507       30152431.98      P      0     0        .000000    10

3505       30152431.98      N      0     0        .000000    10

514       30152431.98      D      0     0        .000000    11

0       30152431.98      P      0     0        .000000    11

Uncrunching matrix

Optimal solution found