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A View of Lagrangian Relaxation and Its Applications

In: Numerical Nonsmooth Optimization

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  • Manlio Gaudioso

    (Universitá della Calabria)

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.

Suggested Citation

  • Manlio Gaudioso, 2020. "A View of Lagrangian Relaxation and Its Applications," Springer Books, in: Adil M. Bagirov & Manlio Gaudioso & Napsu Karmitsa & Marko M. Mäkelä & Sona Taheri (ed.), Numerical Nonsmooth Optimization, chapter 0, pages 579-617, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34910-3_17
    DOI: 10.1007/978-3-030-34910-3_17
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