Answers to: Solving SOCP in CPLEX, cannot find solutionhttp://www.or-exchange.com/questions/15126/solving-socp-in-cplex-cannot-find-solution<p>Hi,</p>
<p>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.</p>
<p>Minimize</p>
<p>obj: 1.9 x1 + 0.3 x2 - 2.1 x3 + 0.3 x6 + 0.7 x7</p>
<p>Subject To</p>
<p>c1: - 2 x1 <= -5</p>
<p>c2: x1 - 2 x2 - x4 <= 1</p>
<p>c3: x1 - 2 x2 + x4 >= 1</p>
<p>c4: x1 + x3 - x5 <= 3</p>
<p>c5: x1 + x3 + x5 >= 3</p>
<p>q1: [ x4 ^2 - x6 ^2 ] <= 0</p>
<p>q2: [ x5 ^2 - x7 ^2 ] <= 0</p>
<p>Bounds</p>
<pre><code> x1 Free
x2 Free
x3 Free
</code></pre>
<p>Generals</p>
<p>x1 x2 x3 </p>
<p>End</p>enMon, 30 Oct 2017 13:49:53 -0400Answer by Mark L Stonehttp://www.or-exchange.com/questions/15126/solving-socp-in-cplex-cannot-find-solution/15128<p>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?</p>
<p>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).</p>
<p>Edit: Whoops, I didn't see Paul's post until I posted.</p>Mark L StoneMon, 30 Oct 2017 13:49:53 -0400http://www.or-exchange.com/questions/15126/solving-socp-in-cplex-cannot-find-solution/15128Answer by Paul Rubinhttp://www.or-exchange.com/questions/15126/solving-socp-in-cplex-cannot-find-solution/15127<p>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 \(M\rightarrow\infty\).</p>Paul RubinMon, 30 Oct 2017 13:36:16 -0400http://www.or-exchange.com/questions/15126/solving-socp-in-cplex-cannot-find-solution/15127