Duality of MILP

Answered

Sagnik Basumallik

• April 12, 2020 20:09
• Edited

I am trying to understand if Gurobi derives lower bounds on the optimal solution value of a MILP problem using dual functions when Branch-and-Cut is used. 

If yes, is there a way to access the dual variables and the lower bounds of the MILP ? 

Additionally, can I retain the cuts to be used for a similar MILP with warm-start?

 

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• 

  Richard Oberdieck

  Gurobi Staff

  • April 14, 2020 12:26

  Dual variables are not well defined for MILPs, as they derive from convex analysis, and MILPs are non-convex due to the presence of integer variables. However, in theory you could fix the binary variables corresponding to a particular solution, solve the resulting LP and then get the values of the dual variables.

  However, as discussed in this knowledge base article, we advise against such strategies as the result carries little meaning. What are you trying to achieve with this?

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