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

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...

Full description

Saved in:
Bibliographic Details
Published inJournal of optimization theory and applications Vol. 178; no. 1; pp. 119 - 130
Main Authors Chen, Yuqing, Zhang, Chuangliang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Continuity (mathematics)
Engineering
Mathematics
Mathematics and Statistics
Minimax technique
Operations Research/Decision Theory
Optimization
Theory of Computation
Vector spaces
49J45
Minimum
Lower semi-continuous from above
von Newman’s minimax principle
Upper semi-continuous from below
49J27
49K35
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1189-x