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There may be some complexity with detecting the variable decomposition (which variables do we predict then project (y) vs solve for (z)) in general. Probably a good default is to use z for variable-in-set constraints and y for the rest.
We should be able to automate DLL for conic problems by using the projections in https://github.com/matbesancon/MathOptSetDistances.jl/blob/master/src/projections.jl. Hopefully we can differentiate through those functions 🤞
There may be some complexity with detecting the variable decomposition (which variables do we predict then project (
y
) vs solve for (z
)) in general. Probably a good default is to usez
for variable-in-set constraints andy
for the rest.Also relevant:
https://github.com/jump-dev/Dualization.jl -- formulate the dual MOI/JuMP model
https://github.com/matbesancon/MathOptSetDistances.jl -- project predicted
y
onto its conehttps://github.com/jump-dev/ParametricOptInterface.jl -- formulate
z
completion problem withy
as parametershttps://github.com/jump-dev/DiffOpt.jl -- differentiate through
z
completion (computedobj/dy
jump-dev/DiffOpt.jl#282)Would also be super cool to detect special cases (e.g. examples 1, 2, 3 in DLL) to handle those efficiently.
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