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

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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.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Augustine O. Esogbue, Qiang Song & Donovan Young

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  1. Augustine O. Esogbue
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  2. Qiang Song
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  3. Donovan Young
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Correspondence to Augustine O. Esogbue.

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Esogbue, A.O., Song, Q. & Young, D. Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems. Math Meth Oper Res 63, 525–542 (2006). https://doi.org/10.1007/s00186-005-0044-2

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  • DOI: https://doi.org/10.1007/s00186-005-0044-2

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