Friday, November 22, 2013

Speeding up the solution of quadratic problems

Over and over again  MOSEK users asks one of the following questions:

  • How should I formulate my quadratic optimization problem so it solves faster?
  • Why does MOSEK say my problem is nonconvex and what can I do about it?
The answer to both questions is that the problem should be reformulated so quadratic terms becomes separable i.e. the Hessian of the quadratic terms should be diagonal matrices. This is always possible and will make the convexity check extremely simple and robust. Moreover, in most cases the problem will also solve faster after the reformulation.

Details about the reformulations tricks can be seen in our whitepaper.