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Lagrangian conditions for vector optimization in Banach spaces

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  • Joydeep Dutta
  • Christiane Tammer

Abstract

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions for weakly efficient solutions of non-convex location problems. Copyright Springer-Verlag 2006

Suggested Citation

  • Joydeep Dutta & Christiane Tammer, 2006. "Lagrangian conditions for vector optimization in Banach spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 521-540, December.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:521-540
    DOI: 10.1007/s00186-006-0079-z
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    Citations

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    Cited by:

    1. Marius Durea & Radu Strugariu & Christiane Tammer, 2013. "Scalarization in Geometric and Functional Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 635-655, December.
    2. Vu Anh Tuan & Christiane Tammer & Constantin Zălinescu, 2016. "The Lipschitzianity of convex vector and set-valued functions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 273-299, April.
    3. Luis Rodríguez-Marín & Miguel Sama, 2013. "Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 683-700, March.
    4. L. Alvarez-Vázquez & N. García-Chan & A. Martínez & M. Vázquez-Méndez, 2010. "Multi-objective Pareto-optimal control: an application to wastewater management," Computational Optimization and Applications, Springer, vol. 46(1), pages 135-157, May.
    5. D. Aussel & J. Dutta, 2011. "On Gap Functions for Multivalued Stampacchia Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 513-527, June.
    6. M. Durea & J. Dutta & C. Tammer, 2010. "Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 196-211, April.

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