GLPK solver with Pyomo, not recognizing infeasibility

Question

I have a simple infeasible problem as below.

• Maximize z = 4x1 + 3x2

• 2x1 - x2 >= 6

• x1 + x2 <= 2

• x1 and x2 >= 0

After solving I see that the termination status says 'ok' rather than saying 'infeasible'. May I know if something is wrong with the formulation in code?

# Create a concrete model
model = ConcreteModel()

# Define variables with initialization and domain
model.x1 = Var(domain=NonNegativeReals, initialize=0.0)
model.x2 = Var(domain=NonNegativeReals, initialize=0.0)

# Define the objective function
model.obj = Objective(expr=4 * model.x1 + 3 * model.x2, sense=maximize)

# Define the constraints
model.constraint1 = Constraint(expr=2 * model.x1 - model.x2 >= 6)
model.constraint2 = Constraint(expr=model.x1 + model.x2 <= 2)

# Solve the model using the GLPK solver
solver = SolverFactory('glpk')
results = solver.solve(model)

Answer 1

This is indeed a little weird! When I run your example, I get the output from GLPK:

GLPK Simplex Optimizer 5.0
3 rows, 3 columns, 5 non-zeros
Preprocessing...
2 rows, 2 columns, 4 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  2.000e+00  ratio =  2.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 2
      0: obj =  -0.000000000e+00 inf =   6.000e+00 (1)
      1: obj =   8.000000000e+00 inf =   2.000e+00 (1)
LP HAS NO PRIMAL FEASIBLE SOLUTION
glp_simplex: unable to recover undefined or non-optimal solution
If you need actual output for non-optimal solution, use --nopresol
Time used:   0.0 secs
Memory used: 0.0 Mb (40412 bytes)

From this it is very clear that GLPK is well aware that there is no primal feasible solution, hence it knows that it is an infeasible problem.

However, results.solver.status says ok and results.solver.termination_condition says other. I have tried to solve the problem with cplex, gurobi, and cbc as well. They report the following

	GLPK	CBC	CPLEX	Gurobi
status	ok	warning	ok	warning
termination_condition	other	infeasible	infeasible	infeasibleOrUnbounded

From this, it seems that there is something going on with what GLPK is returning as the termination condition to Pyomo. The other solvers are capable of conveying the message that your model does not have an optimal solution.