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On the Weak Semi-continuity of Vector Functions and Minimum Problems

Author

Listed:
  • Yuqing Chen

    (Guangdong University of Technology)

  • Chuangliang Zhang

    (Guangdong University of Technology)

Abstract

Lower semi-continuity from above or upper semi-continuity from below has been used by many authors in recent papers. In this paper, we first study the weak semi-continuity for vector functions having particular form as that of Browder in ordered normed vector spaces; we obtain several new results on the lower semi-continuity from above or upper semi-continuity from below for these vector functions. Our results generalize some well-known results of Browder in scalar case. Secondly, we study the minimum or maximum problems for vector functions satisfying lower semi-continuous from above or upper semi-continuous from below conditions; several new results on the existence of minimal points or maximal points are obtained. We also use these results to study vector equilibrium problems and von Neumann’s minimax principle in ordered normed vector spaces.

Suggested Citation

  • Yuqing Chen & Chuangliang Zhang, 2018. "On the Weak Semi-continuity of Vector Functions and Minimum Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 119-130, July.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-017-1189-x
    DOI: 10.1007/s10957-017-1189-x
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    References listed on IDEAS

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    1. P. Q. Khanh & D. N. Quy, 2012. "On Ekeland’s Variational Principle for Pareto Minima of Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 280-297, May.
    2. P. Khanh & D. Quy, 2011. "On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings," Journal of Global Optimization, Springer, vol. 49(3), pages 381-396, March.
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    Cited by:

    1. Zhang, Chuang-liang & Huang, Nan-jing & O’Regan, Donal, 2023. "On variational methods for interval-valued functions with some applications," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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