A View of Lagrangian Relaxation and Its Applications

Manlio Gaudioso ()
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Manlio Gaudioso: Universitá della Calabria

Chapter Chapter 17 in Numerical Nonsmooth Optimization, 2020, pp 579-617 from Springer

Abstract: 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34910-3_17

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DOI: 10.1007/978-3-030-34910-3_17

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