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Some minimax problems in lexicographic order

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Abstract

In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y) = u(x)+β(x)v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.

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Authors and Affiliations

  1. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, China

    Yu Zhang

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Sheng-jie Li

Authors
  1. Yu Zhang
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  2. Sheng-jie Li
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Correspondence to Sheng-jie Li.

Additional information

Supported by the National Natural Science Foundation of China (No. 11171362, 11571055).

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Zhang, Y., Li, Sj. Some minimax problems in lexicographic order. Acta Math. Appl. Sin. Engl. Ser. 33, 193–200 (2017). https://doi.org/10.1007/s10255-017-0650-9

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  • DOI: https://doi.org/10.1007/s10255-017-0650-9

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