Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and bound bound methods for solving certain classes of nonconvex optimization problems by reducing the duality gap. We discuss this method for the class of partly linear and partly convex optimization problems and, incidentally, point out incorrect results in the recent literature on this subject.
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Tuy, H. On Solving Nonconvex Optimization Problems by Reducing The Duality Gap. J Glob Optim 32, 349–365 (2005). https://doi.org/10.1007/s10898-004-1947-9