How does Gurobi determine whether a MIQCQP problem is feasible or not

Answered

Sixiong You

• March 05, 2020 21:04

Hi, I am working on the mixed-integer quadratically constrained quadratic programmings (MIQCQP), and I found that when I randomly generated some nonconvex MIQCQP problems, the Gurobi can tell me quickly if this problem is infeasible or not, I am wondering why Gurobi can be so efficient to judge whether a problem is feasible or not, or is it possible gives me some wrong information? 

Thanks

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  Yuriy Zinchenko

  Gurobi Staff

  • March 06, 2020 00:44

  Generally speaking, Gurobi will apply same "branch and cut" approach as for the MIP, e.g., see here for very basic explanation, https://www.gurobi.com/resource/mip-basics/

  It sounds we are just very efficient on your models :)

   

  Hope this helps,

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  Sixiong You

  • March 06, 2020 21:19

  

  

  

  Thanks for your fast reply! I have read the recommended website, and it is helpful. 

  And I have one more question, just for the mixed-binary quadratic constrained programming (maybe nonconvex), is it possible that GUROBI will take a long time to tell whether this model is feasible or not? 

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  Yuriy Zinchenko

  Gurobi Staff

  • March 09, 2020 16:00

  It is certainly possible that the solver takes a while -- non-convex MIQP can be very challenging.

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