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On cone characterizations of weak, proper and Pareto optimality in multiobjective optimization

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  • Kaisa Miettinen
  • Marko M. Mäkelä

Abstract

Efficient, weakly and properly Pareto optimal solutions of multiobjective optimization problems can be characterized with the help of different cones. Here, contingent, tangent and normal cones as well as cones of feasible directions are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:2:p:233-245
    DOI: 10.1007/s001860000109
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    Citations

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    Cited by:

    1. M. M. Mäkelä & Y. Nikulin, 2009. "On Cone Characterizations of Strong and Lexicographic Optimality in Convex Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 519-538, December.
    2. Alexander Engau, 2017. "Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 119-134, January.
    3. M. Zarepisheh & E. Khorram, 2011. "On the transformation of lexicographic nonlinear multiobjective programs to single objective programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 217-231, October.
    4. 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.

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