unbounded status returned for infeasible problem

[mlubin]

With the following Julia code, I build two problems. The first one is declared unbounded (although I know it's infeasible). The second problem is the same as the first, except with a zero objective. This one is properly declared infeasible.

import ECOS
import MathProgBase

I = [1,1,2,5,3,4,7,1,2,3,4,5,6,7,8]
J = [1,2,2,2,3,3,3,4,5,6,7,8,9,10,2]
V = [1.0,-3.0,1.0,-2.0,-1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0]
A = sparse(I,J,V)

b = [0.0,10.0,1.0,1.0,0.0,1.0,9.0,10.0]
c = [-1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
var_cones = [(:Free,1:3),(:Zero,4:4),(:NonNeg,5:5),(:SOC,6:8),(:NonNeg,9:9),(:NonNeg,10:10)]
constr_cones = [(:Zero, 1:length(b))]

m = MathProgBase.model(ECOS.ECOSSolver(verbose=1))
MathProgBase.loadconicproblem!(m, c, A, b, constr_cones, var_cones)
MathProgBase.optimize!(m)

@show MathProgBase.status(m)

m = MathProgBase.model(ECOS.ECOSSolver(verbose=1))
MathProgBase.loadconicproblem!(m, zeros(length(c)), A, b, constr_cones, var_cones)
MathProgBase.optimize!(m)

@show MathProgBase.status(m)

The output on my machine is:

ECOS 2.0.2 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS

It     pcost       dcost      gap   pres   dres    k/t    mu     step   sigma     IR    |   BT
 0  -3.000e+01  -3.000e+01  +3e+01  2e-01  3e-01  1e+00  6e+00    ---    ---    1  1  - |  -  - 
 1  -3.000e+01  +1.528e+02  +2e+01  7e+01  2e+01  2e+02  3e+00  0.6243  3e-01   1  1  1 |  0  0
 2  -3.000e+01  -2.386e+01  +1e+00  5e+00  3e-01  7e+00  2e-01  0.9542  1e-02   1  1  1 |  0  0
 3  -3.000e+01  +6.259e+02  +1e-02  1e+01  3e-01  7e+02  2e-03  0.9890  1e-04   2  2  2 |  0  0
 4  -3.000e+01  +5.940e+04  +1e-04  1e+01  3e-01  6e+04  2e-05  0.9890  1e-04   4  3  3 |  0  0
 5  -3.000e+01  +5.376e+06  +1e-06  1e+01  3e-01  5e+06  3e-07  0.9890  1e-04   6  5  5 |  0  0
 6  -2.999e+01  +4.863e+08  +2e-08  1e+01  3e-01  5e+08  3e-09  0.9890  1e-04   1  1  1 |  0  0

UNBOUNDED (within feastol=9.5e-09).
Runtime: 0.000319 seconds.

MathProgBase.status(m) => :Unbounded

ECOS 2.0.2 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS

It     pcost       dcost      gap   pres   dres    k/t    mu     step   sigma     IR    |   BT
 0  +0.000e+00  -0.000e+00  +3e+01  2e-01  6e-01  1e+00  6e+00    ---    ---    1  0  - |  -  - 
 1  +0.000e+00  +1.828e+02  +2e+01  7e+01  2e+01  2e+02  3e+00  0.6243  3e-01   1  1  1 |  0  0
 2  +0.000e+00  +6.140e+00  +1e+00  5e+00  3e-01  7e+00  2e-01  0.9542  1e-02   1  1  1 |  0  0
 3  +0.000e+00  +6.559e+02  +1e-02  1e+01  3e-01  7e+02  2e-03  0.9890  1e-04   2  2  2 |  0  0
 4  +0.000e+00  +5.943e+04  +1e-04  1e+01  3e-01  6e+04  2e-05  0.9890  1e-04   3  3  3 |  0  0
 5  +0.000e+00  +5.376e+06  +1e-06  1e+01  3e-01  5e+06  3e-07  0.9890  1e-04   7  5  5 |  0  0
 6  +0.000e+00  +4.863e+08  +2e-08  1e+01  3e-01  5e+08  3e-09  0.9890  1e-04   1  1  1 |  0  0

PRIMAL INFEASIBLE (within feastol=1.6e-10).
Runtime: 0.000239 seconds.

MathProgBase.status(m) => :Infeasible

[mlubin]

Just tested on 2.0.4, no change in behavior.