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Some saddle-point theorems for vector-valued functions

Author

Listed:
  • Nguyen Xuan Hai

    (Posts and Telecommunications Institute of Technology)

  • Nguyen Hong Quan

    (Posts and Telecommunications Institute of Technology)

  • Vo Viet Tri

    (Thu Dau Mot University)

Abstract

This paper concerns with vector saddle point problems where the image space of the objective bifunction is not endowed with any topology and the orders in the image space are defined from general sets. Some new existence results of vector saddle points are established based on using notions of vector-cyclic quasimonotonicity together with notions of “algebraic” semicontinuity, without assuming convexity assumptions.

Suggested Citation

  • Nguyen Xuan Hai & Nguyen Hong Quan & Vo Viet Tri, 2023. "Some saddle-point theorems for vector-valued functions," Journal of Global Optimization, Springer, vol. 86(1), pages 141-161, May.
  • Handle: RePEc:spr:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01250-z
    DOI: 10.1007/s10898-022-01250-z
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    References listed on IDEAS

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    1. Y. Zhang & S. Li, 2013. "Minimax theorems for scalar set-valued mappings with nonconvex domains and applications," Journal of Global Optimization, Springer, vol. 57(4), pages 1359-1373, December.
    2. F. Flores-Bazán & C. Vera, 2006. "Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 185-207, August.
    3. Dorel Duca & Liana Lupsa, 2012. "Saddle points for vector valued functions: existence, necessary and sufficient theorems," Journal of Global Optimization, Springer, vol. 53(3), pages 431-440, July.
    4. Gutiérrez, C. & Jiménez, B. & Novo, V., 2012. "Improvement sets and vector optimization," European Journal of Operational Research, Elsevier, vol. 223(2), pages 304-311.
    5. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    6. Daniel Gourion & Dinh Luc, 2014. "Saddle points and scalarizing sets in multiple objective linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 1-27, August.
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