Replacing variables with constants

[rb004f]

in discussions with @jac0320 we noticed that in some cases bound tightening reduced variables to constants. To improve performance, we could replace variables with constants.

Suggested architecture: We can use our relaxation pattern matching architecture that already replaces constraints with their relaxation. In this case we look for any constraint that has a variable whose ub = lb, and replace that constraint with the "relaxed constraint" where that variable is replaced with a constant

[jac0320]

The above proposal should goes into bound_propagation() as a special feature. Using bound_propagation(), m.l_var_tight and m.u_var_tight will be updated. These keeps the tighten bounds (using any method, Bound Propagation, BT, PBT...) for constructing local NLP model and bounding model.

For discrete variables, if ub==lb, replace var with parameters during model construction utilizing the affine constraint structure.

For continuous variables, if isapprox(ub, lb; atol=10e-8) == true, then assign var with ub/2+lb/2. This might need more discussion.

[jac0320]

Another comment: directly doing this is not as easy as it seems. As the model is parsed into MPB for upper bound search, deleting a variable is not easy since the abstraction layer is fairly raw. But this definitely motivates a different design of data structure which has more control of the raw model data.

[kaarthiksundar]

Can lead to numerical issues. Leave the onus on the user to remove redundancies.