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On Cone Characterizations of Strong and Lexicographic Optimality in Convex Multiobjective Optimization

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  • M. M. Mäkelä

    (University of Turku)

  • Y. Nikulin

    (University of Turku)

Abstract

Various type of optimal solutions of multiobjective optimization problems can be characterized by means of different cones. Provided the partial objectives are convex, we derive necessary and sufficient geometrical optimality conditions for strongly efficient and lexicographically optimal solutions by using the contingent, feasible and normal cones. Combining new results with previously known ones, we derive two general schemes reflecting the structural properties and the interconnections of five optimality principles: weak and proper Pareto optimality, efficiency and strong efficiency as well as lexicographic optimality.

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  • 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.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:3:d:10.1007_s10957-009-9570-z
    DOI: 10.1007/s10957-009-9570-z
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    References listed on IDEAS

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    1. Igor V. Konnov & Dinh The Luc & Alexander M. Rubinov, 2006. "Generalized Convexity and Related Topics," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-37007-9, October.
    2. 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.
    3. Dehui Yuan & Altannar Chinchuluun & Xiaoling Liu & Panos M. Pardalos, 2007. "Optimality Conditions and Duality for Multiobjective Programming Involving (C, α, ρ, d) type-I Functions," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 73-87, Springer.
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    Cited by:

    1. 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.

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