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Relaxations of Multilinear Convex Envelopes: Dual Is Better Than Primal

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Experimental Algorithms (SEA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7276))

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Abstract

Bilinear, trilinear, quadrilinear and general multilinear terms arise naturally in several important applications and yield nonconvex mathematical programs, which are customarily solved using the spatial Branch-and-Bound algorithm. This requires a convex relaxation of the original problem, obtained by replacing each multilinear term by appropriately tight convex relaxations. Convex envelopes are known explicitly for the bilinear case, the trilinear case, and some instances of the quadrilinear case. We show that the natural relaxation obtained using duality performs more efficiently than the traditional method.

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Author information

Authors and Affiliations

  1. LIX, École Polytechnique, 91128, Palaiseau, France

    Alberto Costa & Leo Liberti

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  1. Alberto Costa
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  2. Leo Liberti
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Editors and Affiliations

  1. CNRS - LaBRI - Université Bordeaux 1, 351 Cours de la Libération, 33405, Talence cedex, France

    Ralf Klasing

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Costa, A., Liberti, L. (2012). Relaxations of Multilinear Convex Envelopes: Dual Is Better Than Primal. In: Klasing, R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30850-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-30850-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30849-9

  • Online ISBN: 978-3-642-30850-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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