Complementary Slackness: Issues with Big-M

Answered

Zhisheng Xiong

August 09, 2025 18:44

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Hi,
I’m using the Big-M technique to linearize the complementary slackness conditions from the KKT system, which turns my optimization model into a MIP (the only integer variables come from these complementary slackness constraints).

When I set M too large, I end up getting only a relaxed solution; but if I set it smaller, Gurobi fails to converge and keeps iterating without termination.

Is there a smarter way to handle this? For example, can using addGenConstrIndicator avoid having to manually choose a Big-M value? Or do you have any other suggestions?

Thanks a lot!

Related to

• Bilinear
• Big-M

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  Riley Clement

  • Gurobi Staff

  August 11, 2025 00:32

  Hi Zhisheng,

  You can use addGenConstrIndicator to avoid choosing a Big M value, but I don't expect this would resolve your problem.

  Your best bet is to try and tune the solver.  I would first try with different combinations of MIPFocus and Presolve and if you want to dive deeper then the following video may help: Introduction to Performance Tuning.

  - Riley

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  Zhisheng Xiong

  August 14, 2025 08:08

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  Hi Riley,

  Thanks for your valuable information. I have checked the code examples and video, and now have some ideas in mind. I will try running my optimization again. 

  Since the solution of the KKT system is used to generate cuts in a decomposition algorithm, if the solution quality is poor, the cuts will be weak—or worse, the whole algorithm may converge prematurely.

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