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Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems

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  • Augustine Esogbue
  • Qiang Song
  • Donovan Young

Abstract

In this paper the problem of verifying the Pareto-optimality of a given solution to a dynamic multiple-criterion decision (DMCD) problem is investigated. For this purpose, some new conditions are derived for Pareto-optimality of DMCD problems. In the literature, Pareto-optimality is characterized by means of Euler-Lagrangian differential equations. There exist problems in production and inventory control to which these conditions cannot be applied directly (Song 1997). Thus, it is necessary to explore new conditions for Pareto-optimality of DMCD problems. With some mild assumptions on the objective functionals, we develop necessary and/or sufficient conditions for Pareto-optimality in the sprit of optimization theory. Both linear and non-linear cases are considered. Copyright Springer-Verlag 2006

Suggested Citation

  • Augustine Esogbue & Qiang Song & Donovan Young, 2006. "Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 525-542, July.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:525-542
    DOI: 10.1007/s00186-005-0044-2
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    References listed on IDEAS

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    1. Kaisa Miettinen & Marko M. Mäkelä, 2001. "On cone characterizations of weak, proper and Pareto optimality in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 233-245, June.
    2. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2005. "Reference point approach for multiple decision makers," European Journal of Operational Research, Elsevier, vol. 164(3), pages 785-791, August.
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