基于改进集的双层向量均衡问题解的存在性
Existence of the Solution for Bilevel Vector Equilibrium Problem via Improvement Sets
DOI: 10.12677/PM.2022.1210170, PDF,    科研立项经费支持
作者: 黄文君, 曾丽华, 高雲霄：江西理工大学，基础课教学部，江西 南昌
关键词: 改进集；双层向量均衡问题；解的存在性；Improvement Sets； Bilevel Vector Equilibrium Problem； Existence of Solution
摘要: 本文研究了改进集下的双层向量均衡问题解的存在性。结合拓扑空间知识，运用改进集的有关结论，在向量Tikhonov-type正则化过程下得到了基于改进集的双层向量均衡问题解的存在性。
Abstract: In this paper, the existence of solution for bilevel vector equilibrium problem is studies under improvement sets. Combining the knowledge of topological space and using the relevant conclusions of the improvement set, the existence of the solution of the bilevel vector equilibrium problem based on the improvement set is obtained under the vector Tikhonov-type regularization process.
文章引用：黄文君, 曾丽华, 高雲霄. 基于改进集的双层向量均衡问题解的存在性[J]. 理论数学, 2022, 12(10): 1571-1576. https://doi.org/10.12677/PM.2022.1210170

参考文献

[1] Chicco, M., Mignanego, F., Pusillo, L. and Tijs, S. (2011) Vector Optimization Problems via Improvement Sets. Journal of Optimization Theory and Applications, 150, 516-529. [Google Scholar] [CrossRef] 
[2] Bonnel, H. and Morgan, J. (2006) Semivectorial Bilevel Optimization Problem: Penalty Approach. Journal of Optimization Theory and Applications, 131, 365-382. [Google Scholar] [CrossRef] 
[3] Bard, J.F. (1998) Practical Bilevel Optimization: Applications and Algorithms. Kluwer Academic Publishers, Dordrecht. [Google Scholar] [CrossRef] 
[4] Dempe, S. (2002) Foundations of Bilevel Programming. Kluwer Academic Publishers, Dordrecht.
[5] Chadli, O., Ansari, Q.H. and Al-Homidan, S. (2017) Existence of Solutions and Algorithms for Bilevel Vector Equilibrium prOblems: An Auxiliary Principle Technique. Journal of Optimization Theory and Applications, 172, 726-758. [Google Scholar] [CrossRef] 
[6] Ding, X.P. (2012) Existence and Iterative Algorithms of Solutions for a Class of Bilevel Generalized Mixed Equilibrium Problems in Banach Spaces. Journal of Global Optimization, 53, 527-537. [Google Scholar] [CrossRef] 
[7] Capata, A. (2021) Existenceof Solutions of Bilevel Strong Vector Equilibrium Problems and Their Applications. Journal of Nonlinear and Variational Analysis, 5, 371-389. [Google Scholar] [CrossRef] 
[8] Hung, N.V. and O’Regan D. (2020) Bilevel Equilibrium Problems with Lower and Upper Bounds in Locally Convex Hausdorff Topological Vector Spaces. Topology and Its Applications, 269, 106939. [Google Scholar] [CrossRef] 
[9] Li, Q.N., Li, Z. and Zemkoho, A. (2022) Bilevel Hyperparameter Optimization for Support Vector Classification: Theoretical Analysis and a Solution Method. Mathematical Methods of Operations Research. [Google Scholar] [CrossRef] 
[10] Aubin, J.P. and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley, New York.
[11] Luc, D.T. (1989) Theory of Vector Optimization. In: Fandel, G. and Trockel, W., Eds., Lecture Notes in Economics and Mathematical Systems, Spring-Verlag, New York. [Google Scholar] [CrossRef] 
[12] Mao, J.Y., Wang, S.H. and Han, Y. (2019) The Stability of the Solution Sets for Set Optimization Problems via Improvement Sets. Optimization, 68, 2168-2190. [Google Scholar] [CrossRef] 
[13] Gutiérrez, C., Jiménez, B. and Novo, V. (2012) Improve-ment Sets and Vector Optimization. European Journal of Operational Research, 223, 304-311. [Google Scholar] [CrossRef] 

为你推荐