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Continuous Multiobjective Programming

  • Chapter
Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 233))

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-0975, USA

    Margaret M. Wiecek

  2. Department of Management Science, Lancaster University, Bailrigg, Lancaster, LA1 4YX, UK

    Matthias Ehrgott

  3. Rowe School of Business, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

    Alexander Engau

  4. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO, 80217-3364, USA

    Alexander Engau

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  1. Margaret M. Wiecek
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  2. Matthias Ehrgott
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  3. Alexander Engau
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Correspondence to Matthias Ehrgott .

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  1. Department of Economics and Business; Portsmouth Business School, Operations & Systems Management, University of Catania; University of Portsmouth, Catania; Portsmouth, Italy

    Salvatore Greco

  2. Department of Management Science, Lancaster University, Lancaster, United Kingdom

    Matthias Ehrgott

  3. Universidade de Lisboa, CEG-IST, Instituto Superior Técnico, Lisboa, Portugal

    José Rui Figueira

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Wiecek, M.M., Ehrgott, M., Engau, A. (2016). Continuous Multiobjective Programming. In: Greco, S., Ehrgott, M., Figueira, J. (eds) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 233. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3094-4_18

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