Questions About Solving Nonlinear Constraints in an Nonlinear Integer Programming Model
AnsweredHi,
I am currently trying to solve nonlinear constraints in the attached Nonlinear Integer Programming model. As you can see, the fourth constraint in this mathematical model is a nonlinear constraint. I understand that Gurobi is designed to solve linear constraints, yet the solution is successfully generated when I solve this model using Gurobi.
I have a few questions regarding this:
 Since I understand that Gurobi cannot solve nonlinear constraints, how is the fourth constraint being handled?
 Does the fact that the variables in the fourth constraint are binary have any impact?
 I can transform the fourth constraint into a linear form, but what are the differences when solving it as a nonlinear constraint versus a linear constraint?
I look forward to your response.
Thank you.
Kim et al.(2024)
 Hyeonji

Hi Hyeonji,
Since I understand that Gurobi cannot solve nonlinear constraints
Indeed it can, this information is outdated.
Does the fact that the variables in the fourth constraint are binary have any impact?
Yes, we have a bilinear solve routine which can be used when the variables are binary. Gurobi introduced support for mixedinteger nonconvex problems with bilinear terms in v9.
How is the fourth constraint being handled?
In version 11 Gurobi introduced support for solving nonlinear models using spatial branchandbound and outer approximation (see FuncNonlinear) as an alternative to the static piecewiselinear approximation of nonlinear constraints supported in earlier versions. Please refer to the documentation of general constraints for more details.
what are the differences when solving it as a nonlinear constraint versus a linear constraint?
For details please see the following resources from our YouTube channel
NonConvex Quadratic Optimization Webinar
Models with Products of Binary Variables Webinar Video
Tech Talk  A Practical Tour Through Nonconvex Optimization
What's New in Gurobi 11.0 (timestamped to new nonlinear functionality) Riley
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Dear Riley,
Thanks for the message!
This actually solves my question.
 Hyeonji
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