1

I have a question about non-convex models. I deal with a Mixed Integer Quadratic problem (non-convex quadratic objective function with linear constraints- product of two continuous variables in the objective function makes it non-convex). I want to know about the exact methods for solving this type of problem to obtain the global optimum?

Hamed
  • 5,867
  • 4
  • 32
  • 56
m. bk
  • 27
  • 1
  • 5
  • 2
    A solver for this is [GloMIQO](http://helios.princeton.edu/GloMIQO/). Otherwise you can use a (more general) global MINLP solver like [Baron](http://archimedes.cheme.cmu.edu/?q=baron) or [Couenne](http://www.coin-or.org/Couenne/). – Erwin Kalvelagen Nov 06 '16 at 08:57

1 Answers1

0

You cannot solve this problem in general like any NP-hard problems. You can solve the problem with a handful of variables by checking every case. However, you cannot solve it in general, i.e., it is not tractable to solve, for large number of variables.

However, there are methods that can be used for obtaining the suboptimal solution to these problems, e.g., Algorithms for Mixed Integer Problems.

Sunghee Yun
  • 722
  • 1
  • 6
  • 11
  • A little clarity could help. – JerodG Feb 16 '20 at 04:23
  • @JerodG I edited my above answer a bit to make it clearer, but I'm not sure whether I did the right thing. Could you let me know which part is not clear? e.g., do you want to understand why it is NOT possible to get the *exact* global solution? Or do you want to know more about specific algorithms? Thank you! – Sunghee Yun Feb 16 '20 at 04:37