Originally posted by: duyuquan2006

When I solved a SOCP(second order cone programming) problem, CPLEX pushed out the following log,
=========================================================
Tried aggregator 1 time.
QCP Presolve eliminated 102 rows and 114 columns.
Aggregator did 46 substitutions.
Reduced QCP has 577 rows, 363 columns, and 1238 nonzeros.
Number of nonzeros in lower triangle of A*A' = 4397
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.00 sec.
Summary statistics for Cholesky factor:
Rows in Factor = 577
Integer space required = 1593
Total non-zeros in factor = 14259
Total FP ops to factor = 831915
Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf Inf Ratio
0 8.7964163e+009 5.5537675e+001 6.97e+004 0.00e+000 8.80e+009 1.00e+000
1 8.7961885e+009 -2.3552719e+005 6.97e+004 0.00e+000 8.80e+009 2.13e-001
2 8.7941369e+009 -2.2900968e+006 6.97e+004 0.00e+000 8.80e+009 2.79e-002
3 8.7904936e+009 -5.9332250e+006 6.97e+004 0.00e+000 8.80e+009 1.10e-002
4 8.7833251e+009 -1.3100377e+007 6.97e+004 0.00e+000 8.80e+009 4.95e-003
5 8.7685428e+009 -2.7873650e+007 6.97e+004 0.00e+000 8.80e+009 2.31e-003
6 8.5300905e+009 -2.6620759e+008 6.97e+004 0.00e+000 8.80e+009 2.41e-004
7 8.0220169e+009 -7.7395379e+008 6.97e+004 0.00e+000 8.80e+009 7.79e-005
8 4.4927750e+009 -4.2997109e+009 6.97e+004 0.00e+000 8.80e+009 1.14e-005
9 6.5814026e+009 -2.1961473e+009 6.97e+004 0.00e+000 8.79e+009 4.39e-006
10 5.6139560e+009 -3.0794862e+009 6.96e+004 0.00e+000 8.78e+009 9.95e-007
11 4.0369679e+009 -4.3122001e+009 6.89e+004 0.00e+000 8.69e+009 3.15e-007
12 4.0109745e+009 -4.0703602e+009 6.62e+004 0.00e+000 8.35e+009 2.55e-007
13 2.5376241e+009 -3.1627884e+009 6.41e+004 0.00e+000 8.09e+009 8.80e-008
14 5.4987315e+009 -6.8524975e+008 4.53e+004 0.00e+000 5.71e+009 2.24e-008
15 5.2333993e+009 -3.8725381e+008 4.94e+004 0.00e+000 6.23e+009 1.87e-008
16 4.3080477e+009 -9.8724241e+008 4.50e+004 0.00e+000 5.67e+009 1.97e-008
17 2.5781153e+009 -1.1402789e+009 4.24e+004 0.00e+000 5.35e+009 2.13e-008
18 1.4094429e+009 -8.3281283e+008 2.98e+004 0.00e+000 3.77e+009 4.31e-008
19 1.1975093e+009 -5.6916538e+008 1.80e+004 0.00e+000 2.27e+009 5.34e-008
20 2.1236005e+008 -1.2667160e+008 1.41e+004 0.00e+000 1.79e+009 2.76e-007
21 5.6110960e+007 -3.1533435e+007 2.72e+003 0.00e+000 3.43e+008 8.95e-007
22 3.6951467e+007 -1.6702672e+007 7.03e+002 0.00e+000 8.88e+007 1.35e-006
23 5.4473469e+006 -2.5503808e+006 4.31e+002 0.00e+000 5.44e+007 8.39e-006
24 2.2667910e+006 -1.0396418e+006 6.43e+001 0.00e+000 8.12e+006 1.97e-005
25 5.1561191e+005 -1.8401559e+005 2.66e+001 0.00e+000 3.36e+006 9.28e-005
26 1.6574466e+005 -5.3375841e+004 5.63e+000 0.00e+000 7.10e+005 2.96e-004
27 9.2200499e+004 -1.5147118e+004 1.76e+000 0.00e+000 2.22e+005 6.04e-004
28 2.3210110e+004 8.7751912e+003 8.64e-001 0.00e+000 1.09e+005 4.49e-003
29 1.6308360e+004 1.0867349e+004 1.16e-001 0.00e+000 1.47e+004 1.19e-002
30 1.2665769e+004 1.1671272e+004 4.38e-002 0.00e+000 5.52e+003 6.51e-002
31 1.1363044e+004 1.0872246e+004 8.01e-003 0.00e+000 1.01e+003 1.12e-001
32 1.0320545e+004 1.0247257e+004 3.98e-003 0.00e+000 5.00e+002 2.83e-001
33 1.0165301e+004 1.0151749e+004 6.31e-004 0.00e+000 7.68e+001 3.67e-001
34 1.0126924e+004 1.0125667e+004 1.42e-004 0.00e+000 1.63e+001 3.95e-001
35 1.0114856e+004 1.0116435e+004 8.09e-005 0.00e+000 3.79e+000 4.02e-001
36 1.0109637e+004 1.0111891e+004 8.47e-005 0.00e+000 9.06e-001 4.05e-001
37 1.0106553e+004 1.0108967e+004 7.75e-005 0.00e+000 2.18e-001 4.06e-001
38 1.0104380e+004 1.0106830e+004 7.18e-005 0.00e+000 5.25e-002 4.06e-001
39 1.0102734e+004 1.0105192e+004 6.35e-005 0.00e+000 1.27e-002 4.06e-001
Barrier time = 0.19 sec.

Barrier - Infeasible: Objective = 1.0102733529e+004
Solution time = 0.19 sec. Iterations = 39

=========================================================================
And when I used the "conflict" command to detect the conflicts,CPLEX pushed the message,

Refine conflict on 1336 members...

Iteration Max Members Min Members
1 1002 0
2 919 0
3 898 0
4 893 0
5 891 0
6 669 0
7 614 0
8 586 0
9 583 0
10 437 0
11 428 0
12 426 0
13 321 0
14 268 0
15 242 0
16 236 0
17 233 0
18 4 0
CPLEX Error 5002: Q in 'q1' is not positive semi-definite.
CPLEX Error 1720: Conflict detection could not reproduce previously found infea
sibility.
Failed to compute conflict.
CPLEX> display conflict all
No conflict exists.
=================================================================================
I cannot detect the feasibility, so could anybody give me some hints? I attach the
model file "vs1.lp".
Many Thanks.
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Originally posted by: SystemAdmin

I don't think your model is infeasible. Unfortunately, if Barrier runs into numerical difficulty it can sometimes be hard to sort out primal and dual feasibility, and the model you presented poses numerical challenge in both the primal (constraint) and dual (objective function) sense.

I am assuming this to be a continuous relaxation (or other subproblem) of a mixed-integer program.

On the primal side, I see constraints like this:
id438: id201 - id224 + 1000000000 id205 <= 999999979
Variable id205 looks like it is meant to be binary (0-1), where if it is zero then the row is meant to be essentially unconstraining, while if one then the row becomes
id438: id201 - id224 <= -21
Big-M formulations like this pose numerical challenge even in a linear model, and in a quadratic model (even though the constraint itself is linear) the propagation of roundoff error can be especially severe. The actual bounds on variables id201 and id224 seem to be quite modest, and so I would recommend a drastic rescaling, for instance something more like:
id438: id201 - id224 + 10000 id205 <= 9979
(In the MIP context, in your Concert program, there may be other approaches that get rid of the artificial values like 10000 entirely.)

As for the dual side, the objective coefficients have a huge range, from 8e+9 down to 4e-2. It seems also that the scaling of the variables is such that those in the objective function may be expected to take values close to zero but slightly above. If those tiny values have meaning, this is probably too much to expect from a numerical solver. I don't have a specific recommendation here, but perhaps your objective function is actually a multi-criterion problem and you could approach the problem by a sequence of solves, also taking care to rescale so that the variables can be expected to take solution values in the range of (say) 1e-2 to 1e+2.
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