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

Yuqing Chen () and Chuangliang Zhang ()
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Yuqing Chen: Guangdong University of Technology
Chuangliang Zhang: Guangdong University of Technology

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 1, No 7, 119-130

Abstract: 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.

Keywords: Lower semi-continuous from above; Upper semi-continuous from below; Minimum; von Newman’s minimax principle; 49J27; 49J45; 49K35 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-017-1189-x

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