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On set-valued optimization problems with variable ordering structure

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  • Marius Durea
  • Radu Strugariu
  • Christiane Tammer

Abstract

In this paper we introduce and investigate an optimality concept for set-valued optimization problems with variable ordering structure. In our approach, the ordering structure is governed by a set-valued map acting between the same spaces as the objective multifunction. Necessary optimality conditions for the proposed problem are derived in terms of Bouligand and Mordukhovich generalized differentiation objects. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:4:p:745-767
    DOI: 10.1007/s10898-014-0207-x
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    References listed on IDEAS

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    1. Huynh Van Ngai & Nguyen Huu Tron & Michel Théra, 2014. "Metric Regularity of the Sum of Multifunctions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 355-390, February.
    2. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    3. S. Li & C. Liao, 2012. "Second-order differentiability of generalized perturbation maps," Journal of Global Optimization, Springer, vol. 52(2), pages 243-252, February.
    4. M. Durea & R. Strugariu, 2013. "Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 587-603, June.
    5. Reinhard John, 2007. "Local and Global Consumer Preferences," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 315-325, Springer.
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    Citations

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    Cited by:

    1. Marius Durea & Radu Strugariu, 2017. "Vectorial penalization for generalized functional constrained problems," Journal of Global Optimization, Springer, vol. 68(4), pages 899-923, August.
    2. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    3. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 947-963, December.
    4. Truong Q. Bao & Lidia Huerga & Bienvenido Jiménez & Vicente Novo, 2020. "Necessary Conditions for Nondominated Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 826-842, September.
    5. Marius Durea & Radu Strugariu & Christiane Tammer, 2017. "On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 738-763, December.
    6. Bettina Zargini, 2022. "Multiobjective Location Problems with Variable Domination Structures and an Application to Select a New Hub Airport," Logistics, MDPI, vol. 6(2), pages 1-13, March.
    7. Elena-Andreea Florea, 2018. "Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 94-118, July.
    8. Jiawei Chen & Elisabeth Köbis & Markus Köbis & Jen-Chih Yao, 2018. "Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 816-834, June.
    9. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 931-946, December.

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