Relaxations executed by gurobi

Answered

Ahmed Al-Shafei

• July 22, 2022 02:16

Hello, 

I have multiple non-linearities in my model both in the objective function and constraint, namely: 

- x*y   Binary variable multiplied by a continuous variable

- x2*x1  Binary variable multiplied by another Binary variable

I wanted to perform some relaxations but I noticed that Gurobi is able to solve the model with the linearities expressed as they are. My question is, does Gurobi handle those automatically ? and what techniques does it generally use ? 

Thank you

0

• 

  Maliheh Aramon

  Gurobi Staff

  • August 02, 2022 02:53

  Hi Ahmed, 

  Yes, if the quadratic expressions include at least one binary variable, the Gurobi Optimizer can be directed to state these expressions in different ways controlled by the parameter PreQLinearize. 

  The Gurobi Optimizer typically linearizes these quadratic expressions by defining new variables and linear constraints. For a detailed description of how the product of binary variables are treated internally by Gurobi, you might want to check the presentation Specialized Strategies for Products of Binary Variables. 

  To get an idea on how to linearize the product of a continuous variable with a binary variable, please check the blog post on Multiplication of a continuous and a binary variable.

  Best regards,

  Maliheh

  1

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