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Some saddle-point theorems for vector-valued functions

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Abstract

This paper concerns with vector saddle point problems where the image space of the objective bifunction is not endowed with any topology and the orders in the image space are defined from general sets. Some new existence results of vector saddle points are established based on using notions of vector-cyclic quasimonotonicity together with notions of “algebraic” semicontinuity, without assuming convexity assumptions.

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Acknowledgements

This paper was supported by Thu Dau Mot university under grant number DT.21.1-015.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam

    Nguyen Xuan Hai & Nguyen Hong Quan

  2. Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City, Binh Duong, Vietnam

    Vo Viet Tri

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  1. Nguyen Xuan Hai
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  2. Nguyen Hong Quan
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  3. Vo Viet Tri
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Hai, N.X., Quan, N.H. & Tri, V.V. Some saddle-point theorems for vector-valued functions. J Glob Optim 86, 141–161 (2023). https://doi.org/10.1007/s10898-022-01250-z

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