Originally posted by: oozaltin

Hi all,

I am trying to solve the following model, which I think has a positive semi definite quadratic constraint (q1), but I am getting the error 5002.

Any help is greatly appreciated.

Minimize
 obj: -110 x1
Subject To
 c1: x1 >= 0.3
 c2: x1 <= 1
 c3: 0.6 x1 + 0.2 x2 + 0.4 x3 + 0.2 x4 + 0.1 x5  = 1
 q1: [ x1 ^2 + x2 ^2 + x3 ^2 + x4 ^2 + x5 ^2 ]  = 1
End

Originally posted by: MaryFenelon

The error message is a bit misleading; what it should say is that the constraint does not describe a convex region due to the equality sign.  CPLEX can only solve on convex regions which are described by both a PSD matrix and an inequality constraint.  We'll see if we can improve the error message.

Your constraint is the surface of a five-dimensional sphere.  If you change the sense of the constraint to "<=" which is the interior and surface of the sphere,  then CPLEX will be able to solve the problem.

I stumbled upon this page in the documentation today which defines convexity and gives an example in two dimensions.  Also, these tools for diagnosing the cause of CPLEX Error 5002 might be useful.

Originally posted by: oozaltin

Thanks a lot to both of your for your suggestions