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I wonder if this technique works well in branch and bound for Mixed Integer Linear Programming applications. They seem to be just applying it to plain LP applications. While there certainly are some use cases for large LPs, it seems like MILP is where the action is.

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I don't see why not. Mixed Integer usually involves ways of setting up the variables for optimization. PDLP appears to use a lot of presovling which I'm sure helps to establish those bounds whether continuous or integer variables.

Branch and bound is all about changing the bounds on a given fractional variable and resolving. It wasn't clear whether you could re-start from the previous solution with the new bound and quickly reoptimize.

First order methods like PDLP tend to warm start much better than interior point. I'm confident Applegate (of Concorde fame, and who worked on huge MIPs at Google when I was there) is thinking about integration in MIP solvers.

Cool, that’s just what I was wondering.

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