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

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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.

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Acknowledgements

The authors are grateful to the editor and the guest editor for their kind advices and helpful suggestions. They are also grateful to the reviewer for his (or her) good comments and kind suggestions.

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Authors and Affiliations

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong, China

    Yuqing Chen & Chuangliang Zhang

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  1. Yuqing Chen
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  2. Chuangliang Zhang
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Correspondence to Yuqing Chen.

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Chen, Y., Zhang, C. On the Weak Semi-continuity of Vector Functions and Minimum Problems. J Optim Theory Appl 178, 119–130 (2018). https://doi.org/10.1007/s10957-017-1189-x

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