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Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone
Journal of Global Optimization ( IF 1.8 ) Pub Date : 2021-07-24 , DOI: 10.1007/s10898-021-01056-5
Nguyen Van Hung 1 , Vicente Novo 2 , Vo Minh Tam 3
Affiliation  

The aim of this paper is to establish new results on the error bounds for a class of vector equilibrium problems with partial order provided by a polyhedral cone generated by some matrix. We first propose some regularized gap functions of this problem using the concept of \(\mathcal {G}_{A}\)-convexity of a vector-valued function. Then, we derive error bounds for vector equilibrium problems with partial order given by a polyhedral cone in terms of regularized gap functions under some suitable conditions. Finally, a real-world application to a vector network equilibrium problem is given to illustrate the derived theoretical results.



中文翻译:

多面锥提供偏序向量平衡问题的误差界分析

本文的目的是建立关于一类向量平衡问题的新结果,该问题具有由某些矩阵生成的多面锥提供的偏序。我们首先使用向量值函数的\(\mathcal {G}_{A}\) -凸性的概念提出了这个问题的一些正则化间隙函数。然后,我们在一些合适的条件下,根据正则化间隙函数,推导出多面锥给出的偏序向量平衡问题的误差界限。最后,给出了向量网络平衡问题的实际应用,以说明推导出的理论结果。

更新日期:2021-07-26
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