Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming

@article{Liu2018ExactDA,
  title={Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming},
  author={Minghui Liu and G{\'a}bor Pataki},
  journal={Mathematical Programming},
  year={2018},
  volume={167},
  pages={435-480}
}
In conic linear programming—in contrast to linear programming—the Lagrange dual is not an exact dual: it may not attain its optimal value, or there may be a positive duality gap. The corresponding Farkas’ lemma is also not exact (it does not always prove infeasibility). We describe exact duals, and certificates of infeasibility and weak infeasibility for conic LPs which are nearly as simple as the Lagrange dual, but do not rely on any constraint qualification. Some of our exact duals generalize… 

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