Abstract The minimax-maximin relations for vector-valued functionals over the real field are studied. An increase in the dimensionality of criteria may result in a violation of some basic relations, for example, in an inequality between maximin and minimax that is always true for classic problems. Accordingly, the conditions for its correctness or violation need to be established. This paper introduces the definitions of set-valued minimax and maximin for multidimensional criteria and with an analogue in the classic minimax inequality. Necessary and sufficient conditions for its correctness and violation are described for two particular types of vector-valued functionals: the bilinear ones and those with separated variables.

中文翻译：

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向量值准则优化问题的极小极大-极小关系

摘要 研究了向量值泛函在实场上的极小极大-极大关系。标准维数的增加可能会导致一些基本关系的违反，例如，在经典问题中总是成立的 maximin 和 minimax 之间的不等式。因此，需要建立其正确或违反的条件。本文介绍了多维准则的集合值极大极小值和极大极小值的定义，以及经典极小极大不等式中的类比。对于两种特定类型的向量值泛函，描述了其正确性和违规的充分必要条件：双线性函数和具有分离变量的函数。