solver return infeasible for a solvable problem #19
Description
Hello,
When I input the attached ISDP problem, the solver returned "infeasible". However, there are some feasible solutions to this problem, such as x_2, x_5, and x_11 are 1, and 0 for the rest variables. What's more interesting is that when I add the 53th constraint x_5>=1, the solver returns "optimal solution found", which is unreasonable since adding constraints will not enlarge the solution space. Could you please provide some guidance? Thanks in advance.
The following is the content of test.dat-s, which is a binary SDP problem.
15
2
4 -52
0 1 2 0 1 2 0 0 0 0 0 0 0 0 0
0 1 1 1 -17834.694217631153
0 1 1 2 165.3057823691147
0 1 1 3 -291.61806365614996
0 1 1 4 -1.0
0 1 2 2 -1834.694217630329
0 1 2 3 -291.61806365605264
0 1 2 4 -2.0
0 1 3 3 -52.08506915514171
0 1 3 4 -1.0
0 1 4 4 -4.0
1 1 1 1 160006.66555574554
1 1 1 2 -1664.7225462411939
1 1 1 3 416.5972337945695
2 1 1 1 -12000.666555574515
2 1 1 2 332.9445092482388
2 1 1 3 -83.3194467589139
3 1 1 1 18667.555407432712
3 1 1 2 -332.9445092482388
3 1 1 3 83.3194467589139
4 1 1 2 -13329.445092483375
4 1 2 2 46685.5524079284
4 1 2 3 833.1944675886523
5 1 1 2 2665.889018496675
5 1 2 2 -1334.4442592900086
5 1 2 3 -166.63889351773045
6 1 1 2 -2665.889018496675
6 1 2 2 4001.9996667218993
6 1 2 3 166.63889351773045
7 1 1 2 -33327.77870354647
8 1 1 2 6665.555740709295
9 1 1 2 -6665.555740709295
10 1 1 2 6665.555740709295
11 1 1 2 -1333.1111481418588
12 1 1 2 1333.1111481418588
13 1 1 2 -6665.555740709295
14 1 1 2 1333.1111481418588
15 1 1 2 -1333.1111481418588
1 2 1 1 1
1 2 2 2 -1
0 2 2 2 -1
2 2 3 3 1
2 2 4 4 -1
0 2 4 4 -1
3 2 5 5 1
3 2 6 6 -1
0 2 6 6 -1
4 2 7 7 1
4 2 8 8 -1
0 2 8 8 -1
5 2 9 9 1
5 2 10 10 -1
0 2 10 10 -1
6 2 11 11 1
6 2 12 12 -1
0 2 12 12 -1
7 2 13 13 1
1 2 14 14 1
7 2 14 14 -1
4 2 15 15 1
7 2 15 15 -1
7 2 16 16 1
1 2 16 16 -1
4 2 16 16 -1
0 2 16 16 -1
8 2 17 17 1
1 2 18 18 1
8 2 18 18 -1
5 2 19 19 1
8 2 19 19 -1
8 2 20 20 1
1 2 20 20 -1
5 2 20 20 -1
0 2 20 20 -1
9 2 21 21 1
1 2 22 22 1
9 2 22 22 -1
6 2 23 23 1
9 2 23 23 -1
9 2 24 24 1
1 2 24 24 -1
6 2 24 24 -1
0 2 24 24 -1
10 2 25 25 1
2 2 26 26 1
10 2 26 26 -1
4 2 27 27 1
10 2 27 27 -1
10 2 28 28 1
2 2 28 28 -1
4 2 28 28 -1
0 2 28 28 -1
11 2 29 29 1
2 2 30 30 1
11 2 30 30 -1
5 2 31 31 1
11 2 31 31 -1
11 2 32 32 1
2 2 32 32 -1
5 2 32 32 -1
0 2 32 32 -1
12 2 33 33 1
2 2 34 34 1
12 2 34 34 -1
6 2 35 35 1
12 2 35 35 -1
12 2 36 36 1
2 2 36 36 -1
6 2 36 36 -1
0 2 36 36 -1
13 2 37 37 1
3 2 38 38 1
13 2 38 38 -1
4 2 39 39 1
13 2 39 39 -1
13 2 40 40 1
3 2 40 40 -1
4 2 40 40 -1
0 2 40 40 -1
14 2 41 41 1
3 2 42 42 1
14 2 42 42 -1
5 2 43 43 1
14 2 43 43 -1
14 2 44 44 1
3 2 44 44 -1
5 2 44 44 -1
0 2 44 44 -1
15 2 45 45 1
3 2 46 46 1
15 2 46 46 -1
6 2 47 47 1
15 2 47 47 -1
15 2 48 48 1
3 2 48 48 -1
6 2 48 48 -1
0 2 48 48 -1
1 2 49 49 1
2 2 49 49 1
3 2 49 49 1
0 2 49 49 1
1 2 50 50 -1
2 2 50 50 -1
3 2 50 50 -1
0 2 50 50 -1
4 2 51 51 1
5 2 51 51 1
6 2 51 51 1
0 2 51 51 1
4 2 52 52 -1
5 2 52 52 -1
6 2 52 52 -1
0 2 52 52 -1
*This is constraint (x_5 >= 1)
*5 2 53 53 1
*0 2 53 53 1
*INTEGER
*1
*2
*3
*4
*5
*6
*7
*8
*9
*10
*11
*12
*13
*14
*15