Linearizing a quadratic objective function

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Abhishek Solomon

2022年11月11日 22:01

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Hello,

I'm fairly new to optimization and Gurobi.

I have the following objective function to be mazimized:

Xi and Xz are both decision variables. How do i linearize this?

Thanks,

Abhishek

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:23

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try Gurobot?
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  Jaromił Najman

  • Gurobi Staff

  2022年11月14日 09:43

  Hi Abhishek,

  You don't have to linearize this yourself. Gurobi is able to solve (nonconvex) quadratically constrained programs. You can just set the NonConvex parameter and let Gurobi do the work.

  Please note that if your \(X\) variables are continuous or integer, then it is best to provide tight lower and upper bounds for best performance.

  If your \(X\) variables are binary, then it might be worth to experiment with the PreQLinearize parameter which controls the linearization strategy for products of binaries.

  Best regards, 
  Jaromił

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  Abhishek Solomon

  2022年11月14日 19:40

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  Thank you Jaromil for your response, really appreciated!

  I'm working on a school project where a quadratic objective function is considered out of scope and hence needs to be linearized. Any help with that would be great!

  Regards,
  Abhishek

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  Jaromił Najman

  • Gurobi Staff

  2022年11月14日 20:05

  Hi Abhishek,

  For the general case where both variables of the product are continuous, please have a look at McCormick envelopes.

  For binary times continuous variable, you could refer to, e.g., this stackexchange post or this blog. There are similar post on various forums explaining all linearization cases.

  Best regards, 
  Jaromił

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