Dealing with big-M constraints
Big-M constraints are a regular source of instability for optimization problems. They are so named because they typically involve a large coefficient that is chosen to be larger than any reasonable value that a continuous variable or expression may take. Here's a simple example:
However, if the modeler has additional information that the variable will never be larger than , then you could reformulate the earlier constraint as:
For cases when it is not possible to either rescale variable or tighten its bounds, an SOS constraints or an indicator constraint (of the form ) may produce more accurate solutions, but often at the expense of additional processing time.