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Continuous multiobjective programming

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Published
Publication date15/05/2016
Host publicationMultiple criteria decision analysis : state of the art surveys
EditorsSalvatore Greco, Matthias Ehrgott, Jose Rui Figueira
Place of PublicationNew York
PublisherSpringer
Pages739-815
Number of pages77
Edition2nd
ISBN (electronic)9781493930944
ISBN (print)9781493930937
<mark>Original language</mark>English

Publication series

NameInternational Series in Operations Research & Management Science
PublisherSpringer
Volume233
ISSN (Print)0884-8289

Abstract

We present our view of the state of the art in continuous multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts in Sect. 18.2. In Sect. 18.3 we summarize properties of efficient and nondominated sets. Optimality conditions are reviewed in Sect. 18.4. The main part of the chapter consists of Sects. 18.5 and 18.6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Sect. 18.7 we discuss specially-structured problems including linear, nonlinear, parametric, and bilevel MOPs. In Sect. 18.8 we present our perspective on future research directions.