On generalized surrogate duality in mixed-integer nonlinear programming Article Swipe

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Benjamin Müller , Gonzalo Muñoz , Maxime Gasse , Ambros Gleixner , Andrea Lodi , Felipe Serrano ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1007/s10107-021-01691-6

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global $$\epsilon $$ -optimality with spatial branch and bound is a tight, computationally tractable relaxation. 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.

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Relaxation (psychology) Integer programming Generalization Linear programming relaxation Mathematical optimization Integer (computer science) Duality (order theory) Linear programming Set (abstract data type) Computer science Nonlinear system Nonlinear programming Mathematics Algorithm Applied mathematics Discrete mathematics Physics Social psychology Psychology Quantum mechanics Mathematical analysis Programming language

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Type: article
Language: en
Landing Page: https://doi.org/10.1007/s10107-021-01691-6
PDF: https://link.springer.com/content/pdf/10.1007/s10107-021-01691-6.pdf
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Cited By: 2
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Related Works: 10
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DOI: https://doi.org/10.1007/s10107-021-01691-6

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Title: On generalized surrogate duality in mixed-integer nonlinear programming

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Language: en

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Publication year: 2021

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Publication date: 2021-07-17

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Authors: Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano

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Landing page: https://doi.org/10.1007/s10107-021-01691-6

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Concepts: Relaxation (psychology), Integer programming, Generalization, Linear programming relaxation, Mathematical optimization, Integer (computer science), Duality (order theory), Linear programming, Set (abstract data type), Computer science, Nonlinear system, Nonlinear programming, Mathematics, Algorithm, Applied mathematics, Discrete mathematics, Physics, Social psychology, Psychology, Quantum mechanics, Mathematical analysis, Programming language

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Cited by: 2

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