How does simplex method solve the MIQP problem?

Answered

Hongmin Zhang

• September 04, 2023 02:36

As my model is an MIQP problem, the Gurobi software's log indicates that the simplex method is being utilized. I am perplexed by how the simplex method is applied to an MIQP problem. Is there any comprehensive documentation available that explains the algorithm in detail? Moreover, if the MIQP problem is relaxed, how can this be implemented? I would greatly appreciate it if you could provide documentation or papers that delve into this aspect of the algorithm.

Related to

• MIQP

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  David Torres Sanchez

  Gurobi Staff

  • September 05, 2023 08:13

  Hi Hongmin,

  The parameters: PreMIQCPForm and PreQLinearize control the transformation being used.
  You might want to have a play with these parameters.
  Additionally see MIQCPMethod.

  Cheers, 
  David

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  Hongmin Zhang

  • September 06, 2023 12:56

  

  

  

  Dear David,

  I believe that the 'PreQLinearize' parameter facilitates the transformation from MIQP (Mixed-Integer Quadratic Programming) to MILP (Mixed-Integer Linear Programming), and I am curious if there is any algorithm documentation that provides a detailed explanation of this process.

  Best wishes,

  Hongmin

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  David Torres Sanchez

  Gurobi Staff

  • September 06, 2023 13:14

  Hi Hongmin,

  Apart from the documentation, you can also find more details about this in the Ed Klotz webinar:

  • Video: https://www.youtube.com/watch?v=qGgJ0gBptwY
  • Slides: https://www.gurobi.com/wp-content/uploads/Models-with-Products-of-Binary-Variables.pdf

  Particularly, see slide 12.

  Cheers, 
  David

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