A geometric study of duality gaps, with applications

@article{Lemarchal2001AGS,
  title={A geometric study of duality gaps, with applications},
  author={Claude Lemar{\'e}chal and Arnaud Renaud},
  journal={Math. Program.},
  year={2001},
  volume={90},
  pages={399-427}
}
Lagrangian relaxation is often an efficient tool to solve (large-scale) optimization problems, even nonconvex. However it introduces a duality gap, which should be small for the method to be really efficient. Here we make a geometric study of the duality gap. Given a nonconvex problem, we formulate in a first part a convex problem having the same dual. This formulation involves a convexification in the product of the three spaces containing respectively the variables, the objective and the… CONTINUE READING
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