On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12125)


Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments.


Surrogate relaxation MINLP Nonconvex optimization 



We gratefully acknowledge support from the Research Campus MODAL (BMBF Grant 05M14ZAM) and the Institute for Data Valorization (IVADO) through an IVADO Postdoctoral Fellowship.


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Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Universidad de O’HigginsRancaguaChile
  3. 3.Polytechnique MontréalMontréalCanada

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