jump-dev / jump-dev/MathOptComplements.jl

Why bridges and not an optimizer

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Description

I'm not convinced about the bridge approach. I know we discussed it and I was interested to see what happened, but after looking at the code I have some reservations.

In particular, many of the reformulations are not exact with the idea that you solve a sequence of problems for decreasing $\tau \rightarrow 0$, warm-starting each solve from the prior solution. The bridge approach doesn't allow that.

I was more thinking along the lines of https://github.com/jump-dev/MultiObjectiveAlgorithms.jl and https://github.com/jump-dev/MathOptLazy.jl, where we cache some part of the model (here, complementarity constraints), and then move all of the complexity into the `MOI.optimize!` routine.

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