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A View of Lagrangian Relaxation and Its Applications

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Numerical Nonsmooth Optimization

Abstract

We provide an introduction to Lagrangian relaxation, a methodology which consists in moving into the objective function, by means of appropriate multipliers, certain complicating constraints of integer programming problems. We focus, in particular, on the solution of the Lagrangian dual, a nonsmooth optimization (NSO) problem aimed at finding the best multiplier configuration. The algorithm for solving the Lagrangian dual can be equipped with heuristic procedures for finding feasible solutions of the original integer programming problem. Such an approach is usually referred to as Lagrangian heuristic. The core of the chapter is the presentation of several examples of Lagrangian heuristic algorithms in areas such as assignment problems, network optimization, wireless sensor networks and machine learning.

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Author information

Authors and Affiliations

  1. Universitá della Calabria, Rende, Italy

    Manlio Gaudioso

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  1. Manlio Gaudioso
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Correspondence to Manlio Gaudioso .

Editor information

Editors and Affiliations

  1. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, VIC, Australia

    Adil M. Bagirov

  2. Department of Informatics, Modeling, Electronics and System Engineering, University of Calabria, Rende (CS), Italy

    Manlio Gaudioso

  3. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Napsu Karmitsa

  4. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Marko M. Mäkelä

  5. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, VIC, Australia

    Sona Taheri

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Gaudioso, M. (2020). A View of Lagrangian Relaxation and Its Applications. In: Bagirov, A., Gaudioso, M., Karmitsa, N., Mäkelä, M., Taheri, S. (eds) Numerical Nonsmooth Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-34910-3_17

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