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Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces

Author

Listed:
  • M. Durea

    (Al. I. Cuza University)

  • J. Dutta

    (Indian Institute of Technology)

  • C. Tammer

    (Martin-Luther-University Halle-Wittenberg)

Abstract

This paper presents some results concerning the existence of the Lagrange multipliers for vector optimization problems in the case where the ordering cone in the codomain has an empty interior. The main tool for deriving our assertions is a scalarization by means of a functional introduced by Hiriart-Urruty (Math. Oper. Res. 4:79–97, 1979) (the so-called oriented distance function). Moreover, we explain some applications of our results to a vector equilibrium problem, to a vector control-approximation problem and to an unconstrainted vector fractional programming problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:1:d:10.1007_s10957-009-9609-1
    DOI: 10.1007/s10957-009-9609-1
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    References listed on IDEAS

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    1. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    2. 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.
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    Cited by:

    1. Y. Gao & S. H. Hou & X. M. Yang, 2012. "Existence and Optimality Conditions for Approximate Solutions to Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 97-120, January.
    2. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    3. C. Gutiérrez & B. Jiménez & V. Novo, 2015. "Optimality Conditions for Quasi-Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 796-820, December.
    4. S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 763-782, June.

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