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# 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} }

- Published 2001 in Math. Program.
DOI:10.1007/PL00011429

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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