Description
The key idea is to extend Pyomo's representation system to enable the expression of matrix/vector representations. While this does not improve the efficiency of Pyomo's core expression system, it would offer users an alternative that is likely more performant. Generally, Matrix/Vector expressions would be smaller, and hence the operations needed to canonicalize them would be a smaller burden when interfacing with solvers.
Note that this we have a preliminary Matrix representation in Pyomo kernel. However, a key element of this approach would be to define a Vector representation for parameters and variables. Or to define a convention for using Pyomo's existing Variable/Parameter objects in that manner. But for the hackathon our goal should be to demonstrate the potential performance win.
NOTE: I think it would make sense to include the use of numpy matrix/vector data and scipy.sparse matrix/vector data in our performance hacking. Many users will naturally gravitate to the use of these data formats, and thus I think it would be a mistake to limit the scope of this activity to custom matrix/vector objects.