Hi, I am solving this SOCP problem with CPLEX. There should be solution in this problem. But cplex shows error:1217, No solution exists. Can anybody help me find out what's wrong? Thanks. Minimize obj: 1.9 x1 + 0.3 x2  2.1 x3 + 0.3 x6 + 0.7 x7 Subject To c1:  2 x1 <= 5 c2: x1  2 x2  x4 <= 1 c3: x1  2 x2 + x4 >= 1 c4: x1 + x3  x5 <= 3 c5: x1 + x3 + x5 >= 3 q1: [ x4 ^2  x6 ^2 ] <= 0 q2: [ x5 ^2  x7 ^2 ] <= 0 Bounds
Generals x1 x2 x3 End asked 30 Oct '17, 12:06 newusername 
Your problem is unbounded. Let \(x=(3, 0, M, 2, M, 2, M)\) for an arbitrarily large (positive) integer \(M\). You can check that it is feasible. The objective value is \(1.9 * 3 + 0.3 * 0  2.1 * M + 0 * 2 + 0 * M + 0.3 * 2 + 0.7 * M = 6.3  1.4 * M\) which becomes arbitrarily negative as \(M\rightarrow\infty\). answered 30 Oct '17, 13:36 Paul Rubin ♦♦ Thank you so much!
(30 Oct '17, 14:07)
newusername

This is not an SOCP. Did you get it to run at all by formulating q1 as abs(x4) <= abs(x6) and q2 as abs(x5) <= abs(x5), which makes this a MILP? The problem is unbounded. For instance, take [x1 x2 x3 x4 x5] = [2.5 1.0 0.5 0.5 0]. Then x6 and/or x7 can be negative of arbitrarily large magnitude, which makes the objective function arbitrarily small (i.e., negative of large magnitude). Edit: Whoops, I didn't see Paul's post until I posted. answered 30 Oct '17, 13:49 Mark L Stone 