Dear friends I deal with a Mixed Integer Quadratic problem in my thesis. the objective function is quadratic and non convex with linear constraints. the objective function contains several terms which are product of two continuous variables and these terms in the objective function makes it non convex.the objective function has the following patern: ∑x_i^2 -∑(x_i * y_i)+ ∑z_j I want to know about the methods for linearization.
asked
m_bk |

Why don't you just use an (MI)QP solver capable of handling non-convex objective, of which there are several?

Thanks for your instance reply. I have coded the problem in gams and use Cplex solver since the obj. function is quadratic and the constraints are linear. and for handling the non convexity I used optimallity target option and set it as 3. Cplex claims that it can obtains the global solution. but the problem is the run time that is too long

So you are hoping for "optimization alchemy" in the form of a linearization which does better than CPLEX? Aside from changing various solver parameters/options, if your model has no integer variables, you also have the choice of optimality target 2 to find local optimum in CPLEX. If you can post details of your model, maybe you should post on the CPLEX forum https://www.ibm.com/developerworks/community/forums/html/forum?id=11111111-0000-0000-0000-000000002059 and ask whether anyone has model formulation or solver option suggestions to improve run time.

You can try using binary variables to model the complementarity conditions and reformulate as MILP, as described in this blog post.