This is an optimisation and not JuMP related question, but I thought it worth asking here. I have a constraint in my model which limits the number of non-negative instances of a variable. Specifically, I have a power balance where there is a slack (load shedding) variable, and I limit the number of times that it can be non-zero:

where lsi_t is a binary variable and eps is a small number to avoid computational issues.

My question is whether there is literature on efficient formulations of the above, similarly to how, say, in unit commitment the formulation with 3 binary variables tends to be more efficient than with only 1. I imagine there must be some operations research literature on the subject, but searching for key words similar to the ones used in the title havenâ€™t proved useful.

Thanks in advance.