电子商务视角下集合优化问题的Levitin-Polyak良定性
Levitin-Polyak Well-Posedness of Set Optimization Problems from the Perspective of E-Commerce
DOI: 10.12677/ecl.2024.133941, PDF,   
作者: 谢林燕：贵州大学数学与统计学院，贵州 贵阳；贵州省博弈决策与控制系统重点实验室，贵州 贵阳
关键词: 电子商务；有限理性；集合优化问题；Levitin-Polyak良定性；E-Commerce； Bounded Rationality； Set Optimization Problems； Levitin-Polyak Well-Posedness
摘要: 在许多经济模型中，决策者需要通过比较集值优化问题的目标函数来衡量支出以达到自身收益的最大。在电子商务视角下，本文讨论了有限理性下基于改进集的集合优化问题E-u-最小解集的Levitin-Polyak良定性和广义Levitin-Polyak良定性，并通过有限理性模型证明了该良定性的充分条件。此外，借助非线性分析的方法给出了集合优化问题(广义) Levitin-Polyak良定性的特征刻画。这些结果为电子商务在实际生活中的应用打下了夯实的理论基础。
Abstract: In many economic models, decision-makers need to measure expenditures by comparing the objective functions of set-valued optimization problems in order to achieve maximum benefit. Under the perspective of E-commerce, this paper studies the Levitin-Polyak well-posedness and generalized Levitin-Polyak well-posedness of E-u-minimal solution of set optimization problems under bounded rationality via improvement set. Furthermore, the sufficient condition of well-posedness is given by using a bounded rationality model. Besides, we obtain the characterization of (generalized) Levitin-Polyak well-posedness for the problem by utilizing nonlinear analysis method. These results have laid a solid theoretical foundation for the application of E-commerce in practical life.
文章引用：谢林燕. 电子商务视角下集合优化问题的Levitin-Polyak良定性[J]. 电子商务评论, 2024, 13(3): 7660-7668. https://doi.org/10.12677/ecl.2024.133941

参考文献

[1] 聂林海. “互联网+”时代的电子商务[J]. 中国流通经济, 2015(6): 53-57.
[2] Aubin, J.P. and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley.
[3] Tikhonov, A.N. (1966) On the Stability of the Functional Optimization Problem. USSR Computational Mathematics and Mathematical Physics, 6, 28-33. [Google Scholar] [CrossRef] 
[4] Levitin, E. and Polyak, B. (1966) Convergence of Minimizing Sequences in Conditional Extremum Problems. Soviet Mathematics—Doklady, 7, 764-767.
[5] Zhang, W.Y., Li, S.J. and Teo, K.L. (2009) Well-Posedness for Set Optimization Problems. Nonlinear Analysis: Theory, Methods & Applications, 71, 3769-3778. [Google Scholar] [CrossRef] 
[6] Gutiérrez, C., Miglierina, E., Molho, E. and Novo, V. (2012) Pointwise Well-Posedness in Set Optimization with Cone Proper Sets. Nonlinear Analysis: Theory, Methods & Applications, 75, 1822-1833. [Google Scholar] [CrossRef] 
[7] Khoshkhabar-Amiranloo, S. and Khorram, E. (2016) Scalarization of Levitin-Polyak Well-Posed Set Optimization Problems. Optimization, 66, 113-127. [Google Scholar] [CrossRef] 
[8] Khoshkhabar-Amiranloo, S. (2018) Characterizations of Generalized Levitin-Polyak Well-Posed Set Optimization Problems. Optimization Letters, 13, 147-161. [Google Scholar] [CrossRef] 
[9] Vui, P.T., Anh, L.Q. and Wangkeeree, R. (2018) Levitin-Polyak Well-Posedness for Set Optimization Problems Involving Set Order Relations. Positivity, 23, 599-616. [Google Scholar] [CrossRef] 
[10] Gupta, M. and Srivastava, M. (2020) Approximate Solutions and Levitin-Polyak Well-Posedness for Set Optimization Using Weak Efficiency. Journal of Optimization Theory and Applications, 186, 191-208. [Google Scholar] [CrossRef] 
[11] Duy, T.Q. (2021) Levitin-Polyak Well-Posedness in Set Optimization Concerning Pareto Efficiency. Positivity, 25, 1923-1942. [Google Scholar] [CrossRef] 
[12] 伍玉涛, 贾文生. 有限理性下集值优化问题的Levitin-Polyak良定性[J/OL]. 系统科学与数学, 2024: 1-9.
https://link.cnki.net/urlid/11.2019.O1.20240228.1254.009, 2024-02-29.
[13] 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] 
[14] Kuroiwa, D. (2001) On Set-Valued Optimization. Nonlinear Analysis: Theory, Methods & Applications, 47, 1395-1400. [Google Scholar] [CrossRef] 
[15] Mao, J., Wang, S. and Han, Y. (2019) The Stability of the Solution Sets for Set Optimization Problems via Improvement Sets. Optimization, 68, 2171-2193. [Google Scholar] [CrossRef] 
[16] Luc, D.T. (1989) Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems. Wiley.
[17] Alonso, M. and Rodríguez-Marín, L. (2005) Set-Relations and Optimality Conditions in Set-Valued Maps. Nonlinear Analysis: Theory, Methods & Applications, 63, 1167-1179. [Google Scholar] [CrossRef] 
[18] 俞建. 关于良定问题[J]. 应用数学学报, 2011, 34(6): 1007-1022.
[19] 俞建. 博弈论与非线性分析[M]. 北京: 科学出版社, 2008.
[20] Kuratowski, C. (1930) Sur les espaces complets. Fundamenta Mathematicae, 15, 301-309. [Google Scholar] [CrossRef] 
[21] 俞建. 有限理性与博弈论中平衡点集的稳定性[M]. 北京: 科学出版社, 2017.

为你推荐