改进集下双层强向量均衡问题的存在性
The Existence of Bilevel Strong Vector Equilibrium Problem under Improved Set
摘要: 本文研究了改进集下的双层强向量均衡问题，运用改进集的相关结论，并结合拓扑空间知识，通过向量Thikhonov-type正则化过程得到了其解的存在性。这在一定程度上推广和发展了已有文献的结论。
Abstract: In this paper, we study the bilevel strong vector equilibrium problem under the improved set. By using the relevant conclusions of the improved set and combining the knowledge of topological space, we obtain the existence of its solution through the vector Thikhonov-type regularization process. This extends and develops the conclusions of the previous literature to a certain extent.
文章引用：黄文君, 曾丽华. 改进集下双层强向量均衡问题的存在性[J]. 理论数学, 2022, 12(11): 1948-1953. https://doi.org/10.12677/PM.2022.1211210

参考文献

[1] Blum, E. and Oettli, W. (1994) From Optimization and Variational Inequalities to Equilibrium Problems. Mathematica Student, 63, 123-145.
[2] Ansari, Q.H. (2000) Vector Equilibrium Problems and Vector Variational Inequalities. In: Giannessi, F., Ed., Vector Variational Inequalities and Vector Equilibria, Kluwer, Dordrecht, Boston, 1-15. [Google Scholar] [CrossRef] 
[3] Bianchi, M., Hadjisavvas, N. and Schaible, S. (1997) Vector Equilib-rium Problems with Generalized Monotone Bifunctions. Journal of Optimization Theory and Applications, 92, 527-542. [Google Scholar] [CrossRef] 
[4] Oettli, W. (1997) A Remark on Vector-Valued Equlibria and Generalized Monotonicity. Acta Mathematica Vietnamica, 22, 213-221.
[5] Gutiérrez, C., Jiménez, B. and Novo, V. (2012) Improvement Sets and Vector Optimization. European Journal of Operational Research, 223, 304-311. [Google Scholar] [CrossRef] 
[6] Bonnel, H. and Morgan, J. (2006) Semivectorial Bilevel Optimization Problem: Penalty Approach. Journal of Optimization Theory and Applications, 131, 365-382. [Google Scholar] [CrossRef] 
[7] Malik, A.S., Boyko, O., Atkar, N. and Young, W.F. (2001) A Compar-ative Study of MR Imaging Profile of Titanium Pedicle Screws. Acta Radiologica, 42, 291-293. [Google Scholar] [CrossRef] [PubMed]
[8] Capata, A. (2021) Existence of Solutions of Bilevel Strong Vector Equilibrium Problems and Their Applications. Journal of Nonlinear and Variational Analysis, 5, 371-389. [Google Scholar] [CrossRef] 
[9] Ranjbar, S., Farajzadeh, A., Yao, J.C. and Zhang, T. (2021) Optimality Conditions for Generalized Vector Equilibrium Problems in Vector Spaces. Journal of Nonlinear and Convex Analysis, 22, 133-147.
[10] 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] 
[11] Aubin, J.P. and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley, New-York.
[12] Luc, D.T. (1989) Theory of Vector Optimization. In: Lecture Notes in Economics and Mathematical Systems, Spring-Verlag, New York, Vol. 319. [Google Scholar] [CrossRef] 
[13] 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] 

为你推荐