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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.
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