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Characterizations of convex and quasiconvex set-valued maps

Author

Listed:
  • Joël Benoist
  • Nicolae Popovici

Abstract

The aim of this paper is to characterize in terms of classical convexity and quasiconvexity of extended real-valued functions those set-valued maps which are K-convex or K-quasiconvex with respect to a convex cone K. In particular, we recover some known characterizations of K-convex and K-quasiconvex vector-valued functions. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Joël Benoist & Nicolae Popovici, 2003. "Characterizations of convex and quasiconvex set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 427-435, August.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:3:p:427-435
    DOI: 10.1007/s001860200260
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    Citations

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    Cited by:

    1. Zhiang Zhou & Wang Chen & Xinmin Yang, 2019. "Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 944-962, December.
    2. Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2017. "Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization," Annals of Operations Research, Springer, vol. 251(1), pages 89-104, April.
    3. M. Chinaie & J. Zafarani, 2013. "Image Space Analysis and Scalarization for ε-Optimization of Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 685-695, June.
    4. A. Takeda & S. Taguchi & R. H. Tütüncü, 2008. "Adjustable Robust Optimization Models for a Nonlinear Two-Period System," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 275-295, February.
    5. Carla Antoni & Mohammed Alshahrani, 2018. "Images, Fixed Points and Vector Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 889-905, June.
    6. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    7. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
    8. Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    9. Davide LA TORRE & Nicolae POPOVICI & Matteo ROCCA, 2008. "Scalar characterization of explicitly quasiconvex set-valued maps," Departmental Working Papers 2008-01, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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