Abstract
The concepts of cone extreme points, cone saddle points, and cone saddle values are introduced. The relation of inclusion among the sets mini x∈X max y∈Y f(x, y), maxi y∈Y min x∈X f(x, y), and the set of all weak cone saddle values is investigated in the case where the image space ℝn off is ordered by an acute convex cone.
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Communicated by P. L. Yu
The author is grateful for the useful suggestions and comments given by Prof. K. Tanaka, Niigata University, Niigata, Japan.
The author would like to thank the referees for their valuable suggestions on the original draft.
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Tanaka, T. Some minimax problems of vector-valued functions. J Optim Theory Appl 59, 505–524 (1988). https://doi.org/10.1007/BF00940312
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DOI: https://doi.org/10.1007/BF00940312