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[FEA] Feasibility Polishing #832

@samuelpmish

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@samuelpmish

Hi, I've got an application where the LPs it generates have been greatly accelerated by cuopt's PDLP solver. However, occasionally the solution does not exactly satisfy the constraints. Some other popular PDLP solvers like cuPDLPx support "feasibility polishing" as a post-processing option to clean up the violated constraints, at the expense of the objective (which would be tolerable for my application).

Is something like this planned (or possible already) in cuopt?

I could imagine a couple different possible interfaces:

  1. an explicit "polishing" post process step with user-specified tolerances
  2. the ability to update constraint objective coefficients and resume PDLP iterations (which would also enable polishing, by setting the objective coefficients to 0 and adjusting tolerances).

What are the advantages and disadvantages of PDLP + polishing versus running the original PDLP solve with tighter tolerances?

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