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

 x1 Free

  x2 Free

  x3 Free

Generals

x1 x2 x3

End

asked 30 Oct '17, 12:06

newusername's gravatar image

newusername
132
accept rate: 0%


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 \(M\rightarrow\infty\).

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answered 30 Oct '17, 13:36

Paul%20Rubin's gravatar image

Paul Rubin ♦♦
14.6k412
accept rate: 19%

edited 30 Oct '17, 13:37

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.

link

answered 30 Oct '17, 13:49

Mark%20L%20Stone's gravatar image

Mark L Stone
447310
accept rate: 15%

edited 30 Oct '17, 13:52

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Asked: 30 Oct '17, 12:06

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Last updated: 30 Oct '17, 14:07

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