Originally posted by: Ji.She

Hi everyone,

I am trying to use cplex to solve a quadratic constraint programming problem. To test how to do this, I formulated a small problem in python 2.7 and attached the script here. The problem itself is very simple and I present it here:

Max c

s.t. Q1: c^2 = a^2 + b^2

      0 <= a <= 10

      0 <= b <= 20

I got an error message when calling the solver, which was: "CPLEX Error  5002: 'Q1' is not convex." 

However, from my understanding, this constraint is definitely convex so I don't know why I still get this error. Would anyone please look at it a bit to see if you may identify the error? Any help is greatly appreciated.

Thank you,

Ji

A quadratic equality constraint can never be convex, see also this section in the manual.

Originally posted by: Ji.She

Hi Daniel,

Thank you so much for your reply and clarification. It's embarrassing I didn't see this by myself when formulating my problem. So, does this mean cplex cannot solve the problem I presented above? The real problem I want to solve has multiple constraints including a quadratic equality constraint.

Thank you,

Ji

Often equality constraints can be turned into inequality. For example, in your case 'c^2 ==' is the same as 'c^2 <=' since you are maximizing c. Unfortunately, that is still not good since the constraint is still not convex (note that the reverse constraint c^2 >= a^2 + b^2 is a second order cone constraint which CPLEX can handle, see here for some other non-psd constraint types CPLEX can handle).

For you model at hand, I'm afraid you will have to reformulate before you can solve with CPLEX.