Abstract
For vector-valued functions, cone saddle points are defined, and some existence theorems for them are established in infinite-dimensional spaces. Most of our results rely on Condition 2.1, which has been given by Sterna-Karwat. In particular, it shows that the scalarization of vector-valued functions plays an important role for the condition. Some interesting examples in infinite-dimensional spaces are presented. Moreover, necessary conditions for the existence of cone saddle points are investigated.
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Communicated by P. L. Yu
The author would like to thank the referees for their valuable suggestions on the original draft.
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Tanaka, T. Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces. J Optim Theory Appl 62, 127–138 (1989). https://doi.org/10.1007/BF00939633
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DOI: https://doi.org/10.1007/BF00939633